(JELUS.doc)

2002-08-12

For the Journal of Economic Literature

The Gains from Pension Reform

by

Assar Lindbeck and Mats Persson1

1 Lindbeck: Institute for International Economic Studies, Stockholm University, and The Research Institute for Industrial Economics, IUI, Stockholm; Persson: Institute for International Economic Studies, Stockholm University. We are grateful for useful comments on earlier versions of this paper from Thomas Eisensee, Laurence Kotlikoff, John McMillan, Dirk Niepelt, Ed Palmer, Agnar Sandmo, Ole Settergren, Kjetil Storesletten and two anonymous referees.

1

The Gains from Pension Reform

1. Introduction

The contemporary discussion of pension reform has been initiated mainly by concern for

the long-term financial viability of existing government-operated pension systems. In

some countries, particularly in Latin America and Eastern Europe, such systems have

more or less broken down. In developed OECD countries, the situation is less dramatic.

In the future, however, serious problems are likely to emerge as a result of anticipated

developments in demography and productivity growth. For instance, while the average

contribution rate in the EU today is 16 percent, a recent report by the EU Commission

(2001) estimates that it has to be increased to 27 percent in 2050 if the present rules are

kept unchanged. Predictions for the United States are usually less gloomy. According the

Social Security Administration (2001), the contribution rate in the U.S. social security

system would have to increase from today’s 12.4 percent to 17.8 percent in order to

balance the system in 2050, again with unchanged rules.2

Needless to say, predictions like these have spurred a host of proposals for pension

reform, some of which have already been implemented. Why, then, is there so much

disagreement on this issue, even among highly competent economists? One reason is

simply that pension reform is a very complex issue. Another is that reform proposals

often combine pension reform itself with various auxiliary fiscal policy measures, often

undertaken to mitigate undesirable side effects.

Our ambition is not to provide a comprehensive survey of the enormous literature in this

field. Instead, we want to highlight some basic principles of pension reform, and to

2 The contribution rate that would be necessary to finance current benefits is 10.5 percent in the U.S.; the difference between this figure and the 12.4 percent in the text reflects the current surplus in the U.S. social security system.

2

disentangle various efficiency, distributional and stability aspects. To avoid getting

bogged down in detail, we base our discussion on a unified analytical framework in the

context of a generic overlapping generations model. Such a model automatically focuses

on real economic transactions (such as consumption and labor supply), rather than

financial recordings (such as government debt). The model also highlights the

distribution of income among generations, which is an important aspect of pension

systems. The overlapping generations framework allows us to illuminate the fact that

many objectives of pension reform could alternatively be brought about by general fiscal

policy, i.e., by an appropriate combination of taxes, transfers and government borrowing

– a point forcefully made in generational accounting (Laurence J. Kotlikoff 2002).

After outlining a taxonomy of pension systems (Section 2), we briefly discuss the

consequences for income distribution, saving and labor supply of introducing a pay-as-

you-go system (Section 3). We then address the effects of reforming such a system

(Section 4). Next, we analyze the consequences of shifting, fully or partially, to an

actuarially fair, funded system (Section 5). Finally, we discuss risk and the risk-sharing

properties of pension systems (Section 6). Section 7 offers a brief summary along with

examples of recent pension reforms and reform proposals in various countries.

2. Mandatory Pension Systems: A Taxonomy

Comparisons of pension systems, and discussions of pension reform, are usually based on

the distinction between defined benefit and defined contribution systems. 3 Instead, for

our purposes, we have chosen a three-dimensional classification: defined contribution vs.

defined benefit, funded vs. unfunded, and actuarial vs. non-actuarial pension systems. By

the term defined contribution we mean that the contribution rate is exogenous while

benefits are endogenous. By contrast, in a defined benefit system, the benefit is either a

3 This distinction is not always very clear. A defined contribution system is often identified as a fully funded, actuarially fair system with an exogenous contribution rate; cf., for instance, Robert Merton (1983), Laurence Thomson (1998), Peter A. Diamond (2002) and the EU Commission (2001). The reason why we

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fixed lump sum or an amount determined by the individual’s previous earnings, implying

that future contribution rates have to be endogenous for the pension budget to balance.

The second dimension, referring to the degree of funding, is straightforward: while in an

unfunded (pay-as-you-go) system aggregate benefits are financed by a tax on currently

working generations, in a fully funded system benefits are financed by the return on

previously accumulated pension funds. The third dimension is somewhat subtler. In the

insurance literature, the term “actuarial” is used to describe two quite different features.

One feature is macroeconomic, and refers to the long-run financial stability (viability) of

the system; a stable system is said to be in “actuarial balance”.4 The other feature is

microeconomic, and refers to the relation (link) between contributions and benefits at the

individual level; we will refer to this feature as “actuarial fairness”. We assume that any

pension system has to be financially stable (i.e., be in “actuarial balance”). But within the

class of financially stable pension systems, different degrees of actuarial fairness may be

chosen.5

Real-world systems are rarely clear-cut in any of these dimensions. They often include

actuarial and non-actuarial, as well as funded and unfunded components. Moreover,

while some elements of real-world pension systems are defined-benefit, others are

defined-contribution. Nevertheless, it is useful to keep all three dimensions separate when

analyzing alternative pension systems. Each dimension highlights an important aspect of

pension systems: risk sharing, aggregate saving, and labor market efficiency.

To begin with, we disregard issues of risk and focus on labor market efficiency and

aggregate saving, hence on the actuarial/non-actuarial and the funded/non-funded

dimensions.6 This gives us four generic pension systems, illustrated in the corners of the

do not use this definition is that we want to separate issues of funding, actuarial fairness, and the exogeneity of contributions or benefits. 4 This terminology is used by, e.g., Diamond (2002). It also coincides with the definition of “actuarial” in Palgrave (1994). 5 The notion of actuarial fairness appears under different guises in the literature. Whereas Kotlikoff (1996, 1998) uses the term “degree of linkage”, Robert Fenge (1995) calls an actuarially fair system “intragenerationally fair”. 6 Basically, the same two dimensions have been emphasized by, e.g., Alan J. Auerbach and Laurence J. Kotlikoff (1987, Chapter 10), John Geanakoplos, Mitchell and Stephen P. Zeldes (1999), and Martin S. Feldstein and Jeffrey Liebman (2002) – although to some extent with different terminologies.

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box (trapezoid) in figure 1. Unfunded (pay-as-you-go) systems can be either completely

non-actuarial (position I) or have strong actuarial elements – what we call “quasi-

actuarial” (position II). Funded systems can similarly be either completely non-actuarial

(position III) or actuarially fair (position IV). While the marginal return on the

individual’s contributions is equal to the market rate of interest in an actuarially fair, fully

funded system, it is equal to the growth rate in the tax base in a quasi-actuarial system

(see section 3.2). Since the growth rate is usually lower than the interest rate, we have

depicted position II as somewhat less actuarial than position IV. Figure 1 is useful not

only in a theoretical context, but also when characterizing actual reforms in various

countries (Section 7), as well as when interpreting the results of numerical simulations of

reforms.

[Figure 1 here]

If the defined contribution/defined benefit dimension were unrelated to the other two

dimensions, both defined-contribution and defined-benefit systems would be found in

each corner of figure 1. It is difficult, although not impossible, to construct systems in

positions II and IV as anything other than defined contribution systems, since pension

benefits are then, by definition, closely tied to contributions.7 In positions I and III, it is

easier to conceive of systems that are either defined contribution or defined benefit.

Our three-dimensional classification facilitates separating the consequences of a pension

system for work incentives (highlighted by the actuarial/non-actuarial dimension), capital

formation (highlighted by the funded/unfunded dimension) and risk sharing (highlighted

by the defined benefit/defined contribution dimension). Regardless of the immediate

objectives of a pension reform, it can often be described as a movement in these three

dimensions. Movements along the first dimension are discussed in Section 4, along the

second in Section 5, and along the third in Section 6.

7 A system that could be characterized as an actuarially fair DB system has, however, been suggested by Franco Modigliani and Maria Luisa Ceprini (2002); we discuss this proposal in subsection 6.2 below.

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3. Introducing a Pay-As-You-Go System

3.1 Arguments for Introducing a Mandatory System

When discussing of pension reform, it is important to recognize the reasons for having a

mandatory system in the first place. A well-known justification is to prevent free-riders

from exploiting the altruism of others.8 Another justification is based on paternalism: a

mandatory system prevents myopic individuals from ending up in poverty in old age.

Traditionally, the term “myopic” refers to individuals who, quite irrationally, do not

realize their need for resources as they grow older. A more recent view of myopic

behavior is that an individual, albeit concerned about future needs, tends to discount the

near future at a higher discount rate than the distant future (such as the retirement period).

At each point in time, he would like to save for retirement, but he continually postpones

commencement of that saving until the next period (like a smoker who decides to quit

smoking “tomorrow” rather than today). This type of discounting, which has been labeled

“hyperbolic” or “quasi-exponential” (in contrast to ordinary, exponential discounting),

has been documented in numerous psychological experiments.9 Since a person of this

type lacks self-discipline, he is well served by some kind of commitment device. It is

sometimes argued that such a device could consist of a mandatory pension system, that

prevents him from procrastinating; this point has been made by David Laibson, Andrea

Repetto and Jeremy Tobacman (1998). So far, however, there does not seem to be any

formal political-economy model that explains how such a self-disciplinary device could

be introduced and maintained by collective decision-making.

Two further arguments for mandatory systems are related to limitations in financial

markets. First, the market for annuities is rather undeveloped, due, for instance, to

adverse selection. Second, a pay-as-you-go system introduces a new type of “asset”, a

pension claim whose yield is tied to the growth in the country’s tax base, and this

8 For a formal treatment of this issue, see Kotlikoff (1989). 9 See the surveys by George-Marios Angeletos et al. (2001) and Shane Frederick, George Loewenstein and Ted O’Donoghue (2002). The mathematical properties of alternative discounting functions and the microeconomic foundations of such functions are discussed in Maria Saez-Marti and Jörgen Weibull (2002).

6

provides an opportunity for better portfolio diversification. This observation serves as a

rationale for having at least some pay-as-you-go component in a country’s mandatory

pension system.

Moreover, there are distributional arguments for a pay-as-you-go system, based on the

well-known fact that the introduction (and expansion) of such a system is a gift to the

first cohorts, paid for by subsequent cohorts in the form of an implicit tax on labor

earnings. One argument simply assumes that a majority of self-interested voters in a

country will opt for a pay-as-you-go system, thereby giving a gift to itself. It may then be

asked why subsequent generations (who will pay for the gift) later on continue to support

the system; this issue has been discussed by Thomas F. Cooley and Jorge Soares (1999).

One conceivable explanation is that workers of generation t fear discontinuing to finance

the retirees of generation t-1 since they would then expect generation t+1 to do the same

to them in the future; this would harm cohorts that have already paid mandatory

contributions for a number of years. Another distributional argument for the introduction

of a pay-as-you-go system that provides a gift to the first generation is altruistic. As the

general standard of living in society at large increased dramatically during the 20th

century, it could be argued that many of the elderly, who had very low incomes during a

large part of their lives, were entitled to share the increased living standard of active

workers. A pay-as-you-go system turned out to be a simple way of achieving this. Let us

look at these issues of intergenerational redistribution more closely.

3.2 Budget Sets with a Pay-As-You-Go System

While the first generation in a mandatory pay-as-you-go system receives a gift, the nature

and size of the implicit tax on subsequent generations depend on the rate of return on

their contributions. In a non-actuarial, fully funded system, the rate of return for the

average individual is equal to the market rate of interest, while the marginal rate of return

to any specific individual is zero. In an actuarially fair, fully funded system, by contrast,

both the average and the marginal returns are equal to the interest rate.

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To clarify the rates of return in pay-as-you-go systems, we use a simple two-period

overlapping generations model where the representative individual in generation t works

during the first period of life, with a wage rate and labor supply . He faces a

contribution rate

tw t

tτ to the pension system, and he receives a pension benefit b in the

second period of life. The return on his contribution is then given by

t

1 /( t treturn b )t t wτ+ = . Letting denote the number of individuals in generation t, a

balanced pension budget requires n b

tn

1 1 1t t t t tn 1twτ + + + += . Substituting b from the budget

balance equation into the expression for the individual’s rate of return yields

t

1 1 1 1 111 (t t t t t

tt t t t t

n wreturn Gn w

1 )τ ττ τ+ + + + +

++ = ≡ + ,

where G denotes the growth rate of the aggregate wage sum. If the contribution rate is

constant across generations, the rate of return is clearly G

1t+

1t+ – a result first derived by

Paul A. Samuelson (1958). In most of this paper, we study situations where τ and G are

constant across generations, which means that the subscripts of these variables may be

suppressed. Since we want to compare different pension systems of the same size, in the

case of non-actuarial systems with exogenous benefits b we also assume that the benefit

level is raised over time so that the system constitutes an unchanged fraction of the

national economy. Under these conditions, the average rate of return in any pay-as-you-

go system is G. In a quasi-actuarial system, both the average and the marginal returns to

the individual are G, while in a completely non-actuarial system, the marginal return is

zero.10

10 If G and τ change over time, the implicit return will differ from G 1t+ . For instance, in a defined-benefit system where benefits are proportional to the individual’s previous earning, the return is the growth rate in the previous period, G . In a system with lump-sum benefits that do not change over time (i.e., where the pension system becomes a smaller and smaller fraction of a growing economy), the rate of return will be equal to the growth rate of the labor force in the previous period,

t

1/t tn n − 1− . See John Hassler and Assar Lindbeck (1997, p. 5).

8

We can now derive the budget constraints of the individual. As before, we use subscripts

to denote the generation, while superscripts now denote the period of life (1 or 2) of the

individual. For instance, and refer to consumption in period 1 and period 2,

respectively, of an individual belonging to generation t. For simplicity, and without much

loss of generality, the individual is assumed to have no labor income in the second period

of life. We also follow the convention in the literature of abstracting from the possibility

that the individual has initial wealth in the first period in addition to labor earnings. In

principle, nothing would change if this assumption were dropped. For brevity, we write

the individual’s earnings 11 Letting R denote the real rate of interest, the budget

set of an individual in any pension system can be written

1tc 2

tc

twty ≡ t

tb

( )2 1(1 ) (1 )t t tc y c Rτ= − − + + , (1)

where b is the individual’s pension benefit. If the system is completely non-actuarial,

hence if

t

t b= tb , the effective marginal tax rate on labor is τ . If, on the other hand, the

system is quasi-actuarial, we have b (1 )t G tyτ= + , where G denotes the rate of change in

the tax base ( , as before, denoting the number of individuals in generation t).

Substituting this into (1) and rearranging, we obtain12

tn yt tn

2 11t t tR Gc y c R

Rτ − = − − + +

1 (1 )

)

. (2)

We see from (2) that a quasi-actuarial pay-as-you-go system implies an effective tax rate

(average and marginal) on labor equal to ( ) /(1R G Rτ − + . Clearly, this marginal tax rate

ty

11 The consequences of including traditional income taxes on labor and capital are discussed in Section 4.2. For the time being, we assume that there are no such taxes. 12 If, instead, the system were actuarially fair and fully funded, substituting b (1 )t R τ= + into (1) would

yield the budget constraint , which is the same budget constraint as if there were no pension system at all. In this sense, an actuarially fair, fully funded system is equivalent to no system whatsoever. This conclusion presumes that the individual is at an internal optimum; corner solutions are considered later.

2 1( )(1t t tc y c R= − + )

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is smaller than the marginal rate, τ , in a completely non-actuarial system. Although the

marginal tax wedges on labor differ between a non-actuarial and a quasi-actuarial pay-as-

you-go system, the average tax rate is the same, namely ( ) /(1 )R G Rτ − + . This

observation is simply a mirror image of the fact that the average return is the same,

namely G, in all generic pay-as-you-go pension systems. We also note that regardless of

the degree of actuarial fairness, a pay-as-you-go system does not introduce any tax wedge

on saving; 13 the individual can still save with the return R. This holds both when R is

unaffected by the pension system (for example, in a small open economy) and when R is

influenced by the system.

Table 1 summarizes how the intergenerational distribution of income depends on the

relation between R and G. Gains are indicated by a plus and losses by a minus sign.

[Table 1 here]

If R > G, which currently is regarded as the normal situation (with a capital stock below

the golden rule level), the first generation gains at the expense of subsequent generations.

In the golden rule case, by contrast, where R = G, the gift to generation 1 does not have

to be paid by any subsequent generations. Disregarding the special difficulties of

evaluating the welfare effects of an enforced change in the time profile of consumption of

liquidity-constrained individuals, the gift to generation 1 thus constitutes a free lunch. As

for the dynamically inefficient case where R < G, not only does generation 1 get a free

lunch, so do subsequent generations as well.

The individual’s budget set is not fully described by equation (1). It is reasonable to

assume that an individual cannot borrow with his pension claims as collateral. Since we

have assumed that the individual has no labor income in period 2, the following

inequality must then also hold:

13 This holds for a generic pay-as-you-go system. Qualification may be required when considering various institutional features in real-world systems. For example, if benefits are means-tested, with benefits falling

10

1 (1 )t tc y τ≤ − . (1’)

That is, the individual’s first-period consumption cannot be larger than his first-period

disposable income. We refer to an individual for whom (1’) is binding as liquidity-

constrained. Such an individual’s behavioral responses to policy changes differ from

those of individuals who are non-constrained. Somewhat paradoxically, most studies of

pension systems do not explicitly consider liquidity-constrained individuals, in spite of

the fact that the systems were originally introduced partly in order to influence the

behavior of such individuals (myopic as well as free riders).

3.3 Does Aggregate Income Change When Introducing a Pay-as-you-go System?

Clearly, when R G≤ , there is an aggregate income gain, since no generation loses.

Hence, when looking at aggregate outcomes, the only analytically interesting case is

when R > G. To begin with, we assume that labor supply and factor prices are exogenous.

It is then straightforward to show that the answer to the question in the headline is “No”

(provided the market interest rate, the marginal product of capital and the

intergenerational discount rate coincide; see below).

We first note that each generation’s aggregate pension benefits are equal to the next

generation’s aggregate contributions:

1t t t tn b n y 1τ + += . (3)

This, in fact, is the very definition of a pay-as-you-go system. But it is also possible to

write equation (3) as

11

11 (1 )t t s s s t

s t

R Gn b n yR R

τ∞

− −= +

−=

+ +∑ . (4)

by the amount of an individual’s wealth holding, there will be a distortion of saving.

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Equation (4) simply says that each generation’s benefits are also equal to the capital value

of the net tax payments of all subsequent generations, the effective tax rate being

( ) /(1 )R G Rτ − + .14

Since this also holds for the special case where t = 1, the introduction of a pay-as-you-go

system is a “wash” for all generations taken together, as long as we abstract from

behavioral adjustment: the gift to the first generation is exactly equal to the capital value

of the losses of future generations. In our simple two-period overlapping generations

model with inelastic labor supply and an exogenous R, there are neither aggregate income

gains nor aggregate income losses to society from introducing a pay-as-you-go system.

This amounts to pure redistribution, where one generation’s income gains are exactly

matched by other generations’ income losses. This is a familiar conclusion in the social

security literature; see, for instance, Feldstein and Liebman (2002). Indeed, it is an

application of well-known equivalence theorems in public finance (Kotlikoff 2002,

section III).

Note that this result is independent of the relative size of R and G. This may seem

counterintuitive since the loss to future generations depends on the difference R – G. A

larger difference between R and G might therefore be expected to make the introduction

of a pay-as-you-go system less favorable. But the algebraic exercise above shows that

this conjecture is false. The economic intuition is straightforward: with a higher interest

rate, the discount rate increases in the same proportion. Thus, the higher opportunity cost

to the individual associated with a pay-as-you-go system when R increases is simply

“discounted away” when we calculate capital values.15 Consequently, our conclusion

14 To show that (4) is equivalent to (3), we substitute (1 )s t

s s t tn y Gn y −= + into (4) and obtain

1

1( )

1

s t

t t t ts t

Gn b R G n y

Rτ

−∞

= +

+= −

+

∑ .

Carrying out the summation to infinity, and rearranging, the right-hand side simplifies to . This is equal to the right-hand side of (3); thus (3) and (4) are equivalent.

(1 )t tn y Gτ +

15 Another issue is whether R should be interpreted as the interest rate before or after capital income tax, when such a tax exists. If we are interested in microeconomic incentives, it is obvious that R should be the after-tax interest rate. A different situation arisis when calculating capital values of gains and losses, as in (4). As pointed out by Feldstein and Liebman (2002), R should then be interpreted as the interest rate before

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about the “wash” also holds when R and G change endogenously, due to general

equilibrium effects, as long as there are no behavioral distortions; this point has also been

made by Kotlikoff (2002, section III). Of course, if the marginal product of capital is

higher than the market interest rate, and if capital formation declines as a result of the

pay-as-you-go system, there may be an economic loss to society – a point made by

Feldstein and Liebman (2002). (The reasons why the market interest rate and the

marginal product of capital may differ are discussed in subsection 5.4.)

So far, we have used the market interest rate R for discounting income among

generations. This seems reasonable enough if we are interested in potential Pareto

improvements, since the changes in aggregate capital values then are crucial. But we

should not confine ourselves to Pareto-sanctioned policy changes. Consequently, it is far

from self-evident that the market interest rate R should be used as the intergenerational

discount rate D.16 For example, if D < R, the gift to the first generation is clearly worth

less than the aggregate costs to all subsequent generations. Instead of being a “wash”, the

introduction of a pay-as-you-go system now results in an aggregate income loss to all

generations taken together. But if D < R actually represents society’s distributional

preferences, it is difficult to explain why a pay-as-you-go system, with a gift to the first

generation, was introduced in the first place. Hence, it may be more natural to assume

that at least those who initially decided to introduce a pay-as-you-go system (rather than a

mandatory funded system) held the view that D > R. With such redistributional

preferences, the introduction of a pay-as-you-go system would constitute an aggregate

gain in terms of subjectively discounted income streams. This point is merely a

reformulation of the earlier mentioned justification for introducing a pay-as-you-go

system, namely to favor the first generation.

capital income taxes. The reason is that the representative individual gets back the capital-tax payments via government spending in one form or another. Thus, even in the presence of capital income taxation, equation (4) holds: the gift to generation 1 is exactly equal to the capital value of the costs imposed on all subsequent generations.

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3.4 Consequences for Labor Supply and Saving

The behavioral effects of introducing a pay-as-you-go pension system are related to two

features of that system: the lump-sum gift to the first generation and the effective tax

( ) /(1 )R G Rτ − + on the labor supply of all subsequent generations. Assuming that the

introduction of a pay-as-you-go system has already been announced during the working

life of the first generation (those who receive a gift), and that leisure is a normal good,

there will be an unambiguous reduction in labor supply of that generation. Clearly, this

effect is not caused by any distortions to the behavior of generation 1; it is a pure income

effect. Shrinkage of the budget sets for subsequent generations, by contrast, implies

counteracting income and substitution effects. Thus the net effect on the labor supply of

subsequent generations is probably rather modest. But it is unavoidable that the

substitution effects will distort the labor supply, regardless of whether it falls, rises or

remains constant. After all, the distortion is tied to the substitution effect. This distortion

is, of course, larger in a completely non-actuarial system, where the marginal tax wedge

is τ , than in a quasi-actuarial system, where it is ( ) /(1 )R G Rτ − + .

The effects on aggregate saving during the lifetime of the first generation are

straightforward in the context of a simple life-cycle model. Sticking to the assumption

that the pay-as-you-go system has been announced during that generation’s working life,

and provided that not only leisure but also consumption is a normal good, the

representative individual of that generation will increase his consumption in both periods.

This holds both for liquidity-constrained and non-constrained individuals. Thus,

aggregate saving falls during the working life of generation 1, again reflecting a pure

income effect, due to the lump-sum gift to that generation.17

There are, however, some qualifications to this simple view, even if we disregard the

issue of liquidity-constrained individuals. It is well known that if Ricardian equivalence

16 This point has been made forcefully by Thomas C. Schelling (1995), who argues that a subjective discount rate should be used instead, thereby reflecting preferences associated with the intergenerational distribution of income. 17 The effects on aggregate saving in the future are somewhat more complex and depend on the composition of the population in terms of liquidity-constrained and non-constrained individuals.

14

holds (Robert J. Barro, 1978), there will be no effect at all on aggregate saving. It is,

however, equally well known that Ricardian equivalence relies on rather unrealistic

assumptions, i.e., that there are no liquidity-constrained individuals, that all individuals

have children, and that taxes are not distortionary. Another qualification is that the

negative effect on labor supply will not only reduce hours of work, but also result in

earlier retirement. This will modify the conclusion above of negative effects on saving,

since the individual is then induced to save more during his active years to finance a

longer retirement period; this is Feldstein’s (1974) “induced retirement effect”.

These considerations abstract from general equilibrium effects on factor prices. In

qualitative terms, they are straightforward. An induced fall in aggregate saving reduces

the capital stock over time, which tends to lower real wages and to raise real interest rates

(except in an economy with a linear production technology or a small economy with

internationally integrated capital markets); see Olivier Jean Blanchard and Stanley

Fischer (1989, Chapter 3). The fall in real wages tends to reduce both consumption and

saving, and perhaps also labor supply, while the rise in interest rates tends to reduce real

investment. In this sense, a pay-as-you-go system “crowds out” real investment also via

general equilibrium effects, in the same way as government debt does.

Thus, theoretical considerations are not sufficient to make unambiguous predictions about

the effects on aggregate saving of introducing a pay-as-you-go system. Most empirical

studies in the US conclude, however, that the introduction resulted in a substantial drop in

private saving and the capital stock. Feldstein (1974, 1996b) estimates the fall in private

saving at about 60 percent. According to a general equilibrium simulation study by

Auerbach and Kotlikoff (1987, Table 10.1), the introduction of the US social security

system led to a decline in the capital stock after twenty years by around 20 percent, and to

a fall in real wages by about 5 percent. While welfare, measured as wealth equivalents,

increased by about half a percentage point for the favored generations, it fell by 4–5

percent for more distant generations. In similar studies for Germany, Bernd

Raffelhüschen (1993) arrived at more or less the same results; for references to other

simulation studies, see Georg Hirte and Reinhard Weber (1997). It should be noted,

15

however, that none of these studies of welfare effects distinguishes explicitly between

liquidity-constrained and non-constrained individuals. Moreover, the calculations do not

include the potential welfare gains for society at large of having a mandatory pay-as-you-

go pension system in the first place.

4. Making the System More Actuarial: A Move from I to II

Most countries contemplating pension reform today start from systems in the

neighborhood of position I in figure 1. Some countries limit their ambitions to marginal

(parametric) reforms by either reducing benefits or raising contribution rates, without

changing the basic rules of the system. Other countries change the benefit rules in an

actuarial direction, while maintaining a pay-as-you-go system; for instance, in a country

where the pension has been based on the best five years of an individual’s working life, it

may now be based on the best 10 or 15 years. Such a change can be characterized as a

horizontal move to the right in figure 1. Still other countries undertake systemic reforms

of their pay-as-you-go systems, by a radical shift from a position close to I to a position

close to II, with individual, so-called notional accounts of pension claims. In the generic

case, these accounts are credited with an annual return equal to G, and the pay-as-you-go

system thus mimics a fully funded system – although with a lower rate of return. James

Buchanan (1968) seems to have been the first to propose such a system. While the main

rationale for introducing a system of this type is to improve the economic efficiency and

financial stability of the pension system, it may also have important consequences for the

distribution of income.

4.1 Efficiency

We saw in Section 3.2 that while the marginal tax wedge on labor is τ in a non-actuarial

system, it is [ ]( ) /(1 ) 1 (1 ) /(1 )R G R G Rτ τ− + ≡ − + +

)R

in a quasi-actuarial system. Shifting

from position I to position II in figure 1 thus reduces the marginal tax wedge on labor by

(1 ) /(1Gτ + + . Is this change large or small?

16

When answering this question, it should be noted that the growth rate and the interest rate

in these expressions refer to entire life spans rather than to single years. A numerical

example illustrates the magnitudes involved.18 Assume that an individual starts to work at

age 20, retires at 64 and lives for another twenty years. On average, he may be said to pay

his contribution at age 42 and receive his pension at age 74. Thus, the value of the

contribution grows for 32 years.

The tax wedge may now be written 32 321 11 (1 ) /(1 )G Rτ − + + , where is the yearly

interest rate. For instance, if

1R

2.0=τ , 02.01 =G and 04.01 =R , a move from a non-

actuarial to a quasi-actuarial pay-as-you-go system reduces the tax wedge by 10.8

percentage points, from 20 to 9.2 percent. Since the tax distortion is proportional to the

square of the tax rate, the reduction in the distortion is larger, the higher is τ . A reduction

in the effective tax rate from 20 to 9.2 percent could thus result in a sizeable efficiency

gain.19 This assumes, of course, that individuals actually perceive the reduction in the tax

wedge, which may not be the case for those who are myopic in the traditional sense of the

term.

Although such a reform creates a positive substitution effect on labor supply, there is no

counteracting income effect for the representative individual, since the average tax rate is

unchanged. Thus labor supply will increase as a result of the reform, and labor earnings

rise (provided real wages do not fall much as a consequence). Hence, aggregate saving is

also likely to increase (out of higher labor earnings), resulting in a gradual rise in the

capital stock, in spite of the fact that the reform has no direct effect on saving. Except in

the case of a linear production technology or a small, open economy, interest rates would

fall and real wages rise. The fall in interest rates, in turn, would accentuate the reduction

in the marginal tax wedge, since )1/()( RGR +−τ will fall as R goes down.

18This discussion was inspired by conversations with Martin Feldstein and Laurence Kotlikoff. 19 The more similar G and , the larger the reduction in the tax wedge. For example, if and

, most of the tax wedge will be removed; it is reduced by 14.6 percentage points (from 20 to 5.4 percent).

1 1R 1 0.02G =

1 0.03R =

17

The reduction in the tax wedge cannot be evaluated realistically without considering the

level of other taxes in the economy. Ideally, effects of the tax implicit in a pension system

should be analyzed within the framework of optimal taxation. If there are taxes on capital

income but not on labor earnings and pensions, the implicit tax rate imposed on labor by

a quasi-actuarial pay-as-you-go system would be smaller than the previously derived rate

( ) /(1 )R G Rτ − +

( ) /(1

. The opportunity cost of being forced to save at the low return G, rather

than R, is lower when there is a tax on capital income. By contrast, if there is a tax on

labor income but not on capital income, the effective tax wedge is obviously larger than

)R G Rτ − + . If there are taxes on both labor and capital income, the size of the tax

wedge depends on the relation between these tax rates.20 In the remainder of our

theoretical discussion, we abstract from such taxes in order to concentrate on factors

related to the pension system itself. Needless to say, numerical simulations should

include all types of taxes.

Obviously, a reduction in the marginal tax wedge affects aggregate labor supply not only

through an increase in hours of work but also through later retirement. The importance of

the latter labor-supply aspect is indicated by the fact that while the statutory retirement

age in the EU countries is usually 65, the actual retirement age is 58-59 years in many

countries, and the average employment rate for the age group 55-64 is as low as 38

percent.21 These figures are probably mainly the result of institutional features in the

pension system, namely heavy subsidies of early retirement, often implying that the

capital value of future pensions cannot be raised by working longer. (Jonathan Gruber

and David A. Wise 1999a and 2002, and Axel Börsch-Supan and Joachim K. Winter

20 If there is a tax t on labor and a tax t on capital, it is easy to show that the effective tax rate on labor is R

(1 ) 11

1 (1 ) 1 (1 ).R

R R

R t G Gt

R t R tτ τ

− − ++ +

+ − + −

Assume t 0.= Then, even if R > G, it may well happen that

(1 )R

R t− is close to G, which would mean that a quasi-actuarial pay-as-you-go system does not impose a marginal tax wedge on labor. 21 European Commission (2001, pp. 175-177). In a cross-country study, Gruber and Wise (1999b, pp. 28.35) have found a positive correlation between the average implicit tax rate and the degree of early retirement. Tryggvi Thor Herbertsson and Michael Orzag (2001, p.10) report that the cost in terms of

18

2001). The entire contribution rate is then, in fact, a tax. Thus, making a system quasi-

actuarial also requires the removal of subsidies to early retirement and the closure of

various “pathways” to retirement (such as generous rules for long-term unemployment,

long-term sick leave, and disability pension for elderly workers). The quantitative

importance of raising the effective retirement age may be substantial. A simulation study

by the European Commission (2001, Table 8, p. 199) concludes that if the effective

retirement age could be increased to 65, GDP per capita in 2050 would be 13 percent

higher than otherwise. As a consequence, the consumption of the working-age population

and of pensioners would increase by 11 and 16 percent, respectively.

A shift to a quasi-actuarial pension system will not only reduce the marginal tax wedge, it

will also make the system more transparent because an individual’s pension wealth would

be continuously recorded in his notional account and reported to him. When considering

his retirement decision, the individual can clearly see that remaining in the labor force for

another year would increase his future yearly pension benefits in three ways (John B.

Williamson 2001, p. 21): first, by including another year’s return on the notional assets

already in his account; second, by adding yet another year’s contribution to the account;

and third, by basing the pension benefit on fewer years of projected life expectancy at the

time of retirement.

But even if all subsidies to early retirement were removed, and the system became

completely quasi-actuarial, the implicit tax wedge would still vary over the life cycle. It

will be higher in early than in late working life.22 Forced saving at a yield lower than R is

reduced GDP due to early retirement amounts to more than 10 percent of GDP for several countries; the OECD average hovers around 6 percent. 22 This can be illustrated in the three-period case. Using the same notations as before, we can write the individual’s budget constraint

1 2 3 1 2 32 2

1 1 1(1 ) (1 )1 1(1 ) (1 )t t t t t tc c c y y b

R RR Rτ τ+ + = − + − +

+ ++ +1 ,

where the benefit is b y . Substituting this into the budget constraint and rearranging, we obtain

3 1 2 2(1 ) (1 )t t tG y Gτ τ= + + +

19

more costly early in life, since contributions are then locked in at a low yield over a

longer period. Thus, even with a rather strong link between contributions and benefits,

such as in the case of a quasi-actuarial pay-as-you-go system, intertemporal substitution

of labor supply will still be prevalent, with incentives to work less when young and more

when old. In an optimal-taxation framework, there is perhaps an argument for letting the

contribution rate τ increase with age in a quasi-actuarial system, in order to bring about

tax smoothing over the life cycle.

Any efficiency gains from reducing the tax wedge on labor have to be compared to

consequences for other dimensions, such as income distribution and income insurance.

We now turn to the redistribution issue, while the insurance aspect is dealt with in

Section 6.

4.2 Distributional Aspects

When shifting from non-actuarial to generic quasi-actuarial benefit rules, it becomes

more difficult to use the pension system for redistribution within generations. But when

comparing such a system to a non-actuarial system, it should be kept in mind that

institutional features, such as tying pensions to the best x or last y years, make today’s

non-actuarial systems less progressive than is usually presumed. Such rules tend to favor

those with a steep lifetime income profile. Since they are often high-income earners in a

lifetime perspective, the rules frequently imply redistribution from low-income to high-

income earners. Indeed, a number of empirical studies indicate that real-world non-

actuarial systems are sometimes hardly progressive at all.23 Moreover, most non-actuarial

systems result in redistribution between genders. In some countries, women (who usually

work fewer years than men) tend to be favored by such systems for the same reason as

2

1 2 3 1 22

1 1 1 1 11 1 1 11 1 1 1(1 )t t t t t

G Gc c c y yR R R RR

τ τ

.+ + + + = − − + − − + + + ++

The effective tax wedge on period 2 labor supply is now ( )1 (1 ) /(1 ) ( ) /(1 )G R R G Rτ τ− + + ≡ − + , just as in

the two-period case analyzed above. The tax wedge on period 1 labor, however, is ( )2 21 (1 ) /(1 )G Rτ − + + , which is higher than the period 2 wedge if R > G.

20

high-income earners are. Bluntly formulated, in such countries, non-actuarial systems

redistribute income from poorly educated men to highly educated women. This

redistribution tends to disappear if the system is made more actuarial. In fact, a shift to a

quasi-actuarial system may not be as regressive as expected when only generic systems

are considered.

In reality, many of the new quasi-actuarial systems also allow pension rights for activities

outside the labor market. The most common examples are parents who stay home to take

care of young children, individuals in higher education, in military service, or those living

on unemployment or disability benefits. Formally, some actuarial properties of the

pension system are retained, but the government pays additional money from the general

budget to the pension system, crediting the notional accounts of these individuals.

Moreover, in Section 7, we discuss how new quasi-actuarial systems are often combined

with a basic, or guaranteed, pension in order to eliminate poverty among the elderly. As a

result, it could well be that dominating distributional objectives within generations may,

in fact, be more accurately achieved by shifting to a quasi-actuarial system, if it is

supplemented by a basic or guaranteed pension. Then, of course, the implicit tax in the

overall pension system will be larger than ( ) /(1 )R G Rτ − + , and the efficiency gain

correspondingly mitigated.

What happens to the distribution of income among generations? Since the return to the

average individual is the same in non-actuarial and quasi-actuarial systems, a shift from

one system to the other does not have any direct effects on the intergenerational

distribution of income. General equilibrium effects may, of course, modify this

conclusion. If the reduction in the marginal tax wedge results in higher earnings due to

increased labor supply (including higher retirement age), saving is boosted indirectly. The

aggregate capital stock would then be expected rise, thereby increasing the welfare of

future generations of workers via higher real wages.

23 See, for example, Liebman (2001) and Julia Lynn Coronado, Don Fullerton and Thomas Glass (2000) on such aspects for the US, and Ann-Charlotte Stahlberg (1990) for the Swedish pension system.

21

4.3 Financial Stability

A pension system is regarded as financially stable if the capital value of expected pension

payments is equal to the capital value of the revenues to the system from contributions.24

The reason why issues of financial stability are problematic is that attempts to guarantee

stability have consequences for income distribution and economic efficiency. If such

consequences could be disregarded, shocks to productivity growth and demography

would not threaten the financial stability of the system, in the sense that stability could be

achieved simply by changes in contribution rates (in a defined benefit system) and in

benefits (in a defined contribution system).

It is often claimed that a quasi-actuarial pension system (sometimes called a “notional

defined-contribution” system) is more financially stable than a non-actuarial system. One

conceivable justification for this view is that such a system mimics a fully funded system

in certain respects. More specifically, a quasi-actuarial system may be equipped with

property rights similar to those of a fully funded system. In an actuarially fair, fully

funded system, the pension is based on the return on the individual’s own contributions,

and pension claims are regularly reported as an individually owned financial asset.

Analogously, in a quasi-actuarial system with individual (so-called “notional”) accounts,

the pension is also based on the individual’s own accumulated contributions – although as

a rule the rate of return differs from the market rate of interest. In neither of these systems

is the individual guaranteed a specific rate of return. The rate of return is, however,

determined by simple and transparent rules: by the market interest rate in an actuarially

fair system, and by the growth rate in the tax base in a quasi-actuarial system. The

argument that a quasi-actuarial system is more stable than a non-actuarial one then seems

to rest on the notion that the public is more likely to accept changes in pensions that are

determined by such rules than by ad hoc government intervention.

The Samuelson (1958) rule, whereby financial stability is achieved in a pay-as-you-go

system if the government provides a rate of return equal to the growth rate in the tax base,

seems simple and transparent enough. It was originally developed in the context of a two-

24 This should hold in the aggregate. For actuarial fairness, it should also hold for the individual.

22

period overlapping generations model, where it holds regardless of whether the variations

in G are due to demographic factors ( ), to changes in hours of work of the

representative individual ( ), or to changes in the representative individual’s real wage

( ).25 In a multi-period overlapping generations context, however, such a rule may not

balance the pension budget in each period (where a period refers to a generation’s

working life).

tn

t

tw

Let us look at a three-period overlapping generations model.26 As before, subscripts

denote the generation, and superscripts the period of life (1, 2 or 3) of the representative

individual in a generation. For instance, is aggregate labor

income of generation t – 1 in its second period of life.

21

211

21

211 −−−−−− ≡≡ tttttt Yynwn

Assume first that the aggregate wage sum grows at the steady-state rate G. At time t, a

permanent technological shock occurs in the productivity level, which favors the skills of

elderly workers and simultaneously renders young workers less attractive on the labor

market than before. In other words, we examine a case where experience gains in

importance. More specifically, suppose that income in period 1 is Y 1(1 )s µ− for

generation , and that income in period 2 is Y1s t≥ + 2 (1 )s µ+ for generation s . (Thus, t≥

isY denotes the hypothetical income if the shock had not occurred, and is assumed to

grow at the rate G.) The growth rate in the aggregate wage sum between periods t and t +

1 is then given by

1 2

11 2

1

(1 ) (1 ) 1t t

t t

Y Y GY Yµ µ ∗+

−

− + +≡ +

+,

25 While several of the countries that have recently implemented quasi-actuarial systems have promised the participants a rate of return on their notional accounts equal to G (i.e., the rate of growth in ), other countries have promised another rate of return. For example, the notional accounts in the new Swedish system guarantee a rate of return equal to the average wage rate, w. This implies that a source of instability has been built into the system in the event of changes in n or , which will be dealt with by an ad hoc “break mechanism” when financial instability threatens.

n w

26 This issue was called to our attention by Ole Settergren; see Salvador Valdés-Prieto (2000) for a more general analysis of this issue.

23

while the growth rate in all other periods is equal to the old steady-state rate G. For this

particular type of shock, the system will run a deficit if the government actually provides

a rate of return equal to G on the notional accounts in period t, and G in all other

periods.27

∗

Other types of shocks, however, may be consistent with financial stability, even in the

multiperiod case. One example is when a productivity shock is confined to young

workers. It is often argued that the IT revolution implies such a shock, to which the

pension system under consideration would be robust.

The main point of these simple examples is that the short-term stability properties of a

specific pension system in the real world cannot always be properly evaluated within the

context of a two-period overlapping generations model. For certain types of shocks, a

multi-period model is a more appropriate analytical tool, and calls for a quantitative

simulation model, in which the stochastic process underlying the disturbances is carefully

specified. From a policy point of view, the simple rule of providing a rate of return on

notional accounts equal to each period’s growth rate does not necessarily guarantee

financial stability in the short run. (It should then be noted, however, that “short run” in

this case refers to the lifetime of a generation.) This means that in some cases the

government may be forced to violate the simple “Samuelson rule” in order to achieve

financial stability.

27 To show this, we denote the two rates of return received by generation t during its two active periods by

1

tx and 2

tx , respectively, and write the condition for budget balance 1 11t tY x 2 2 2 1 2

2 1( )(1 ) (1 )(1 ) (1 ) (1t t t t tx Y x Y Y )τ τ µ τ µ τ+ ++ + + + + = − + +

(1Y + 21t+

µ . Substituting Y for Y and

for Y , one sees immediately that this equation is satisfied for

1 2(1 )t G+1 2

t t

12t+

2t )G x x G= = if 0µ = . It is easy

to show that for 0µ > 2

t, setting x G= implies that the other root must satisfy (1 1) (1t )(x G 1 )µ+ = + − .

24

4.4 Overall Assessment

A shift from a completely non-actuarial pension system (of defined benefit type) to a

quasi-actuarial system (of defined contribution type) tends to increase efficiency in the

labor market. Moreover, the possibilities to redistribute income within generations

disappears in principle. But this problem may not be very serious in reality, because

many high-income groups in existing non-actuarial systems have special advantages and

because quasi-actuarial systems can be combined with special features, including a basic

pension or a guaranteed pension. Finally, it is likely that the financial stability of the

system will be greater in a quasi-actuarial than in a non-actuarial system. The reason

would be that in the former type of system, the individuals have only been promised a

rate of return equal to the growth rate in the tax base, regardless of what the growth rate

happens to be.

Another issue is whether a shift from a non-actuarial to a quasi-actuarial system can

result in a Pareto improvement. This question may be formulated as a general question

regarding the design of the tax/transfer system. Assume an affine tax function, defining

disposable income as wtbydisp )1( −+= , where b . Suppose we want to cut the tax

rate t for efficiency reasons, and reduce the intercept b correspondingly, in order to

maintain budget balance. Clearly, if all individuals are identical, everyone would gain if b

were reduced to zero28 – abstracting from income risk. This would also be the case if the

income difference among individuals were sufficiently small, since low-income

individuals would then gain more from removal of the tax distortion than they would lose

from less redistribution. By continuity, this holds up to a certain size of the reduction in b.

For a given value of pre-tax income inequality, b has to be kept above a certain minimum

level so as not to harm low-income groups.

0≥

Let us now apply this general analysis of tax functions to our earlier discussion of

pension reform. A generic non-actuarial pension system corresponds to the affine tax

GComparing this condition to the expression for 1 in the text, it can be shown that for budget balance,

must be smaller than G since the absolute value of clearly is smaller than unity. ∗ 2 1 2 11 1( ) /( )t t t tY Y Y Y+ −− +

∗+1tx

25

function above, with b > 0 and τ=t

)R+

. A quasi-actuarial pension system corresponds to the

case b = 0 and 1/()( GRt −=τ . Thus, a shift from a non-actuarial to a quasi-actuarial

pension system can be described simply as a shift from an affine to a linear tax function.

Our analysis suggests that a partial shift to a quasi-actuarial system, supplemented by a

basic pension b , can result in a Pareto improvement if b is made large enough.

5. Shifting to a Funded System: A Move from II to IV

Three often-mentioned arguments for shifting to a funded system will be discussed

below: i) the individual would receive a higher return on his mandatory saving; ii)

aggregate national saving would increase; and iii) better risk diversification of pension

claims could be achieved. The first two arguments are addressed in this section, and the

third in Section 6. Two other arguments, both of which are conspicuous in the political

discussion of pension reform, are not dealt with in this paper. One maintains that a shift

to a funded system will contribute to a larger and more developed domestic capital

market, thereby increasing efficiency in the allocation of real investment. This was a

prominent argument in discussions of the shift to a mandatory, funded system in Chile in

the 1980s. A more ideological argument is that a mandatory, funded system will make the

entire population stakeholders in equities; this could heighten tolerance for private

ownership and the profitability of firms.29

In a shift from a quasi-actuarial to an actuarially fair, fully funded system, an individual

will experience two changes in his budget constraint: he will receive a market return on

his mandatory savings (rather than a return equal to the growth rate in the tax base), and

he may have to pay a new tax in order to honor the claims of the old pay-as-you-go

28 Whether t should be reduced all the way down to zero depends on whether the government has to finance other expenditures, too. 29 One special aspect of these two arguments has been emphasized by Andrew W. Abel (2001). He argues that if transaction costs are high in the stock market, pension funds with considerable economies of scale in such transactions will make the stock market accessible to small investors. The weight of this argument may have diminished in recent years, in the sense that cheap retail outlets for mutual funds are now available to everyone.

26

pensioners. This new tax could, of course, be imposed on any tax base, such as income or

consumption. For the time being, let us assume that the tax is applied to labor earnings

only, in analogy with the contribution rate in the old pay-as-you-go system.30

Let denote the post-reform per capita pension benefit actually granted to the

representative individual in the last pay-as-you-go generation, generation T. The

aggregate pension payment to that generation after the reform then is n b . In the case

where all old pay-as-you-go claims are fully honored,

T̂b

ˆT T

T̂b bT= , where b is the per capita

pension originally promised to generation T under the old pay-as-you-go system. If,

instead, the claims are not fully honored, generation T would make a loss n b .

T

ˆT T T Tn b−

Denoting the new tax rate of generation s by sθ , the tax vector 1 2 3( , , , ...)T T Tθ θ θ θ+ + +≡

has to satisfy the budget constraint

11

1ˆ(1 )T T s s s s T

s Tn b n y

Rθ

∞

− −= +

=+∑ . (6)

We start with a mechanical calculation of gains and losses for all generations, assuming

labor supply to be exogenous (as in subsection 3.3 on the consequences of introducing

pay-as-you-go system). Our next step is to take behavioral adjustments into account.

Finally, we look at general equilibrium effects including the consequences for factor

prices.

5.1 Does the Shift Give Rise to an Aggregate Income Gain?

Under the same conditions as in subsection 3.3 the answer is “No”. This can be shown in

a very compact way if we disregard behavioral adjustment among individuals. As a result

of the reform, the representative individual in generation has to pay the new tax 1s T≥ +

30 In fact, the choice of tax base and the issue of compensating old pension claims are related. For instance, unlike a payroll tax, income taxes and consumption taxes also hit the old pay-as-you-go pensioners.

27

s syθ , in addition to the contribution syτ ∗ , in his first period of life. We here use τ ∗ to

denote the post-reform contribution rate, which may or may not be equal to the old

contribution rate, τ . In his second period, instead of receiving a pay-as-you-go pension

(1sy )Gτ + , he now receives a funded pension (1 )sy Rτ ∗ + . The present discounted value

(PDV) of the change in disposable income then is

s syθ−

PDV

τ ∗

1

11 (1s s TR R

PD τ θ − −+ +−

V

1

11 (1 )s s TR RR G

− −+ +−

PDΣ

1sR G

Rτ −= +

.

The reason why this capital value is independent of is that the new system is

actuarially fair. The discounted sum over all generations from generation T + 1 is

1s s

s T

R GV n y∞

= +

− Σ = ∑ . (7)

)

To evaluate Σ , we rewrite the budget equation of the old pay-as-you-go system (4),

with t = T, as

PD

1

T T ss T

n b n yτ∞

= +

= ∑ . (8)

Substituting the right-hand sides of (6) and (8) into (7), we obtain

. ˆT T T Tn b n b V− =

In other words, if the pay-as-you-go system is replaced by a fully funded system, and

generation T is not completely compensated, the income loss to that generation would be

exactly equal to the capital value of the income gains to all subsequent generations. If,

instead, generation T is fully compensated (i.e., all claims are honored), the capital value

28

of all future gains would be zero. Note that this conclusion holds regardless of the time

profile of the new tax vector ( ...),, 321 +++ TTT θθθ . A shift from a quasi-actuarial to an

actuarially fair system will not result in a Pareto gain in terms of income. This

conclusion, which has been reported by several authors,31 is hardly surprising since all

conceivable behavioral adjustments have so far been assumed away. Again, this holds

regardless of the size of the difference R – G. The result is a mirror image of our earlier

result (subsection 3.3) that when a pay-as-you-go system is introduced, the income gain

to the privileged generation is exactly equal to the capital value of the income losses to all

subsequent generations.

5.2 Intergenerational Redistribution

While there is no aggregate income gain, and hence no Pareto improvement, some

generations will lose and others gain from the reform depending on the time profile of the

tax-rate sequence ...),,( 321 +++ TTT θθθ and hence on the combination of tax financing and

debt financing of the old pay-as-you-go claims. For simplicity, we assume that the θ

vector is such that the old pay-as-you-go claims are fully honored; thus equation (6) holds

with b . Among such T̂ b= T θ vectors, a useful benchmark case is that the government

borrows exactly as much as is required to set sθ equal to the implicit tax rate under the

old pay-as-you-go system:

,1sR G s T 1

Rθ θ τ −

= ≡ ∀ ≥ ++

. (9)

If, instead, sθ θ> for small values of s, and sθ θ< for large values of s, we call the θ

vector front-loaded, since a relatively large tax burden is placed on the generations

immediately after the removal of the pay-as-you-go system. In this case, there will be

only a moderate build-up of government debt. In the extreme case with 1Tθ τ+ = there

will be no debt at all, since the first generation has to bear the entire burden of honoring

31 See, for instance, Nicholas Barr (2000), Feldstein (1995), Peter R. Orszag and Joseph E. Stiglitz (2001), Robert J. Shiller (1999), Hans-Werner Sinn (2000) and Diamond (2002).

29

the claims of the old pay-as-you-go pensioners; 0=sθ for all . Individuals in

generation T + 1 would pay just as much as before to the preceding generation, although

now without receiving any pension benefit in return later on. In the context of pension

reform, it is usually said that in this case, individuals in generation T + 1 have to pay a

“double contribution”. Their total payment

2s T≥ +

1 1 + T Tyθ 1yTτ ∗+ +

1

+ to the pension system then

becomes , which is equal to 1Ty yτ τ ∗+ + 1T + 2 Tyτ + for the case where τ τ=∗ . By contrast,

the θ vector is back-loaded if sθ θ< for small values of s, and sθ θ> for large values

of s. Such a vector means that considerable government debt will be built up, and a

relatively large burden will be placed on future generations.

θ

D R≠

θ

1

11 s T

1s TWPDV

∞

1 (s )R D − −= +

Σ = ∑ + +

(1

θ

The concepts of front-loaded and back-loaded vectors are crucial when analyzing the

consequences of pension reform for aggregate saving and labor market distortions. It is,

however, also useful when studying the income gains and losses of different generations

when the intergenerational discount rate . It is tempting to conjecture, as in

Feldstein (1995) and Feldstein and Liebman (2002), that the discounted value of the

income gains to all subsequent generations will be positive if a subjective discount rate D

< R is used.32 The conjecture does not hold in general, however. Whether the discounted

income sum is positive or negative also depends on the time profile of the vector. This

can be shown as follows. With D rather than R as the intergenerational discount rate,

equation (7) becomes

s sR G n yτ θ− −

, (7’)

expressing the welfare-weighted income sum with the discount factors 1/ 1)s TD − −+ as

intergenerational weights. There are two cases where this expression is zero: the

benchmark case when s θ= (regardless of the relative sizes of D and R), and the case

when D = R (as shown in section 5.1, regardless of the shape of the θ vector). If the θ

32 This would have been a parallel to our earlier result that the introduction of a PAYGO system reduces the aggregate capital value of income when D < R.

30

vector is front-loaded, and the subjective discount rate is smaller than the market rate, it

follows that (7’) is positive, and hence an aggregate income gain is brought about.33

5.3 Behavioral Adjustments: A Positive Analysis

Let us now allow for behavioral adjustment. Our starting point is the change in the budget

constraint when shifting to a fully funded system. The new constraint is simply obtained

by deducting the new tax payment s syθ from equation (1) and setting (1 )s sb y Rτ= + .

This gives

, (10) ( )2 11 (1 )s s s sc y c R s Tθ = − − + ≥ 1+

1 (1 )s sc y sτ θ∗≤ − − , (10’)

where, as before, the last inequality reflects the assumption that borrowing with expected

future pensions as collateral is not allowed. Here,τ ∗ denotes the contribution rate, and

hence the size, of the funded system that replaces the pay-as-you-go system (where the

contribution rate was τ ).

First, we consider those who are not liquidity-constrained, i.e., individuals for whom

inequality (10’) is not binding. We see that the new contribution rate does not appear in

their post-reform budget constraint (10). This reflects the fact that for a non-constrained

individual, an actuarially fair system is equivalent to no system at all. All behavioral

responses, therefore, depend solely on the new tax rate, sθ . In the benchmark case, when

( ) /(1s )R Gθ θ τ= ≡ − + R

, the individual’s post-reform budget constraint (10) looks the

same as the pre-reform constraint (2). Thus, in this special case, there are no effects on

either labor supply or aggregate saving. Private saving of non-constrained individuals

33 The reason why Feldstein (1995) and Feldstein and Liebman (2002) obtain the result that a shift to a funded system increases the welfare-weighted income sum WPDVΣ if D < R is that front-loading is implicit in their analysis. They assume that the absolute per capita tax payment is constant across generations while the tax base is growing, which means that the tax rate sθ falls over time. There is one more case when , namely when and the 0WPDVΣ > D R> θ vector is back-loaded. For all other configurations of (D, R) and the θ vector, the result of increased funding is either a wash or a loss.

31

would increase, but the effects on aggregate national saving are fully offset by reduced

government saving, since the benchmark tax vector θ requires the government to borrow

in order to finance the old pay-as-you-go claims. A shift from a quasi-actuarial pay-as-

you-go system to a fully funded, actuarially fair system, where the old pay-as-you-go

claims are financed by the benchmark θ vector, is equivalent to no reform at all.

Abstracting from liquidity-constrained individuals, a shift to a fully funded system is not

sufficient for aggregate saving to increase; we also need some assumptions about the

shape of the θ vector.34 It is, however, natural to expect that a front-loaded θ will reduce

consumption of non-constrained individuals and hence increase national saving.35

There is an interesting trade-off between saving and distortions of labor supply. A front-

loaded θ vector tends to increase aggregate saving by reducing the post-reform private

consumption of early generations (provided consumption in both periods of life is a

normal good), at the cost of a larger distortion of labor supply of these generations.

Variations in the time profile of the θ vector thus redistribute both labor-market

distortions and consumption across generations. The consequences for labor supply are

likely to be modest for both early and late generations, since the income and substitution

effects work in opposite directions. The increased saving, which could be substantial,

applies only to those generations for which sθ θ> (as long as liquidity-constrained

individuals are disregarded). Later generations will increase their consumption and hence

contribute to a reduction in aggregate saving.

For the liquidity-constrained individuals, behavioral responses are driven by the

constraint (10’). This means that the degree of front-loading of the θ vector is not

important per se for these individuals. Their consumption will fall if the post-reform

constraint (10’) is tighter, for given earnings, than the pre-reform constraint (1’), i.e., if

34 Political economy considerations may modify this conclusion. For instance, Martin S. Feldstein and Andrew Samwick (2001) assume that the government may ultimately use a budget surplus for increased spending. In such a case, aggregate national saving may rise if a budget surplus is transferred to individual pension accounts. 35 There is a complication here since labor supply may also change, which may lead to an increase in consumption due to higher earnings. We would expect this effect to be rather small, however, due to counteracting income and substitutions effects.

32

sτ θ∗ + >τ , which may well be the case for some cohorts even with a back-loaded θ

vector.

θ

There are thus two ways to augment aggregate saving in connection with a shift to a fully

funded system. One method is to squeeze liquidity-constrained individuals in early

generations by setting *s+ .τ θ τ> The other is to squeeze both liquidity-constrained and

non-constrained individuals in early generations by a front-loaded θ vector.

This discussion relies on a simple life-cycle model. Several modifications of this model

have been suggested in the literature on pension reform. If Ricardian equivalence applies,

a front-loaded θ vector would have no effect on aggregate saving; altruistic parents

would reduce their bequests by the same amount as the tax increase. Thus, to the extent

there are “Ricardian” individuals, the increase in aggregate saving is mitigated. Another

modification is Feldstein’s (1974) “induced retirement effect”. Since a front-loaded

vector will stimulate earlier retirement, the fall in consumption is accentuated, hence also

the rise in aggregate saving. In other words, “Ricardian” effects and induced retirement

effects modify the conclusions of the life-cycle models in different directions when a pay-

as-you-go system is replaced by a fully funded system. Moreover, specific institutional

arrangements in various countries affect labor supply and savings decisions. When

studying pension reform in a specific country, it is therefore important to take explicit

account of such arrangements; this is, in fact, usually attempted in numerical simulation

models.

So far, this discussion of behavioral adjustments to a shift to a funded system has

abstracted from general equilibrium effects. The effects on real wages and interest rates

are straightforward. Except for the case of a back-loaded θ vector, aggregate saving will

increase, and so will the capital stock. As a result, real wages will rise, and real interest

rates will fall36 – except for the extreme case of a linear production technology, or a small

36 In theoretical general equilibrium analyses of pension reform, strongly simplifying assumptions are necessary to obtain manageable results. For instance, Diamond (1997) assumes exogenous labor supply in his general equilibrium analysis.

33

open economy for which interest rates are exogenously given by the world market. Thus

the tendency for disposable income to decline as a result of a front-loaded θ vector will

be counteracted by rising wages, which boost both private consumption and private

saving. The fall in interest rates is usually assumed to reduce saving (although the effect

is theoretically ambiguous). Of course, the quantitative importance of these general

equilibrium effects cannot be assessed without numerical simulations; cf. subsection 5.5.

5.4 Behavioral Adjustments: A Normative Analysis

The result in subsection 5.2 that a shift to a fully funded system cannot give rise to an

aggregate income gain, when we sum over all generations, relied on the assumption that

there are no behavioral adjustments. Let us now look at the possibility of increasing

economic efficiency, and of achieving a Pareto improvement, when such adjustments are

taken into account. Of course, this could always be achieved if the old pension claims

were financed by a lump-sum tax, rather than by a distortionary θ vector.37 But since this

is unrealistic, the basic problem of the transition would simply be assumed away.

Fenge (1995) addressed the Pareto question in a model without liquidity-constrained

individuals. Formally, he assumed that the old pay-as-you-go system is retained, but that

an actuarially fair, fully funded system is added on top of it. Clearly, this cannot result in

any Pareto improvement because, in this case, a fully funded actuarially fair system is

equivalent to no system at all; this result has also been derived by Breyer (1989). At first

glance, it may seem as if Fenge did not actually study a shift from a pay-as-you-go to a

fully funded system, since he retains the pay-as-you-go system. But his experiment is, in

fact, equivalent to abolishing the pay-as-you-go system and financing the transition by

the benchmark vector θ . As we have seen, such a reform has no behavioral

37 This is the approach used by Stefan Homburg (1990) and Friedrich Breyer and Martin Straub (1993) to achieve a Pareto improvement when shifting from a pay-as-you-go to a fully funded system.

34

consequences for non-constrained individuals. Thus there is no possibility of Pareto

improvement. 38

Fenge’s (1995) analysis was limited to what we have called the benchmark vector θ . Is

there some other θ vector that could result in a Pareto improvement? In the analytically

trivial case where the economy is located on the “wrong” side of the Laffer curve for at

least one generation, this is of course possible. But then the tax rate should be reduced for

that generation anyway, regardless of whether a pension reform is in the offing or not.

Taking general equilibrium effects into account, a lower tax rate for one generation may

also lead to higher real wages for future generations, via higher saving from increased

labor earnings. Disregarding the possibility of “Laffer effects”, such a policy will create a

temporary budget deficit. But higher wages for future generations would make it possible

to raise higher tax revenue from these generations, thereby amortizing the government

debt, without harming their welfare. Although this would constitute a Pareto

improvement, such a policy should also be pursued independently of pension reform,

since the income tax is obviously suboptimal to begin with.

But can a net gain to the national economy be achieved by mandatory pension saving?

Moreover, can such a gain be distributed to all generations, so that a Pareto improvement

is achieved? If the rate of return on capital were equal to the market interest rate, the gain

in present-value terms from increasing the capital stock would obviously be zero. But

Feldstein (1996a) and Feldstein and Liebman (2002) have argued that the marginal

product of real capital, ρ , may be greater than the market rate of interest, R. Clearly,

additional investment, yielding a rate of return ρ , discounted by the discount rate R ρ< ,

will then have a positive present value and hence bring about a net income gain to society

as a whole. One explanation for such a difference between the marginal product of capital

38 The same result has been derived formally in a somewhat different context by Kotlikoff (2002, Section III) and Antonio Rangel (1997). The result illustrates the earlier mentioned equivalence theorems in public finance; cf. Henning Bohn (1997) and Kotlikoff (2002).

35

and the market rate of interest may be that a corporate income tax drives a wedge

between these variables:39

(1 )ct Rρ − = . (11)

An obvious conclusion is that a removal of the wedge would eliminate the distortion,

boost capital formation and increase aggregate income in the economy. A first question

then is whether increased funding in the pension system could serve as a complement to a

reduction in t . A second question is whether increased funding could be a substitute for

a reduction in .

c

tc

The answer to the first question is that forced aggregate saving would free economic

resources for investment by reducing the consumption of early generations.40 The

justification for this may be that all resources for domestic investment cannot be

imported. In the presence of non-tradeables, reduced domestic consumption is necessary

to avoid tendencies to increased inflation. A Pareto improvement is not possible,

however, because squeezing the consumption of some generations requires that they are

not compensated later on; if they were, their life-time resources would remain unchanged,

and there would be no initial reduction in their consumption.41

Suppose, however, that it is politically impossible to lower the corporate income tax and

that the government instead tries to use increased funding as a substitute. In an open

economy, the real capital stock is independent of domestic saving, and thus increased

domestic saving would only increase the financial claims on the outside world. It is

therefore not possible to exploit the difference between ρ and R by shifting to a funded

system. In a closed economy, squeezing early generations does lead to a higher domestic

39 This explanation has been emphasized by Feldstein (1996a) and Feldstein and Liebman (2002). 40 This could be brought about either by a front-loaded θ vector (for non-constrained individuals) or by a flat, or even somewhat back-loaded θ vector that makes the constraint tighter for liquidity-constrained individuals. 41 For liquidity-constrained individuals, initial consumption can be squeezed even if their initial income loss is fully compensated later on. The effect on the utility they experience is a moot question, however.

36

capital stock via falling interest rates, but these early generations cannot be compensated.

If they were, their consumption would not decline, and there would thus be no room for

increased capital formation. The conclusion is that a Pareto improvement is impossible

when increased funding is used as a substitute for a reduction in the corporate income

tax.42

There may be another type of efficiency argument for increased funding. If the capital

stock is below the golden rule level, it may be advantageous to increase it. This could in

principle be achieved by a pension reform with a front-loaded θ vector (in the case of a

closed capital market). It should be noted, however, that the golden rule refers to

efficiency in a long-run steady state, which means that movement toward a golden rule

level does not imply a Pareto improvement. Future generations will certainly gain from

such a policy, but it is unavoidable that present generations lose.

This brings us to distributional justifications for a shift to a funded system. One such

argument builds on the observation that a number of cohorts granted gifts to themselves

not only when the pay-as-you-go system was initially introduced, but also when the

contribution rate was gradually increased. These policies raise an ethical question, in the

sense that many of the losing generations had no voting rights – indeed may not even

have been born – when the policy decisions were taken.

A shift to a funded pension system, with a front-loaded θ vector, would be a way to

“claw back” some of the gains from those cohorts that were responsible for the

introduction and expansion of a pay-as-you-go system. Such a policy, however, would be

a rather blunt instrument. First, in order to hit those who gained from the introduction and

are now retired, we would need an income tax or a consumption tax, rather than a higher

payroll tax. Second, unless the θ vector could be made age-dependent, not only older

42 Another proposal to boost capital formation in the connection with a pension reform has been presented by Pascal Belan, Philippe Michel and Pierre Pestieau (1998). Their reasoning is based on an endogenous growth model with a positive externality in capital formation, and they show that a Pareto improvement can in fact be achieved by abolishing the pay-as-you-go system, letting people rely on subsidized private pension saving instead. In the context of this model, where liquidity constraints on individuals are not

37

workers (who may have been favored by the pay-as-you-go system), but also younger

cohorts (who were disfavored) would have to pay the front-loaded extra tax.

Sinn (2000) has put forward another redistributional argument for increased mandatory

saving. He suggests policies that boost the accumulation of physical capital in order to

compensate for the fall in human capital accumulation due to low fertility of the currently

active generation. Since this generation decided to have fewer children than earlier

generations, which could be regarded as a breach of an implicit intergenerational

contract, it should be forced to pay an extra contribution, which is invested in pension

funds.

5.5 Numerical Simulations

A partial step towards a quantitative general equilibrium analysis of pension reform in the

U.S. has been taken by Feldstein and Samwick (1998). They assume endogenous labor

supply and capital formation, while factor prices are exogenous.43 The initial situation in

their study is represented by a pay-as-you-go system with weak linkage between

contributions and benefits (90 percent of the contribution rate τ is a tax) and by other

taxes on labor summing to 20 percent. The old pension claims are assumed to be fully

honored, and are financed by a payroll tax.

In their basic scenario, Feldstein and Samwick assume a growth rate in the tax base of 2.5

percent, and a return on real capital of 9 percent. The large difference between rates of

return in the two systems explains why they obtain relatively large post-reform welfare

gains for future generations at a rather modest cost to the early generations. The long-run

contribution rate could be reduced drastically, from 12.4 to somewhat more than two

considered, the same Pareto gain could, however, be achieved simply by subsidizing private saving without abolishing the pay-as-you-go system. 43 The first numerical simulations with endogenous factor prices were carried out by Laurence S. Seidman (1986) under the same assumption of exogenous labor supply as in theoretical general equilibrium models. He assumed that the claims of the old pay-as-you-go pensioners are not fully honored. Since this would harm the older and benefit the younger cohorts, he did not conduct a Pareto experiment. For reasonable parameter values for the U.S., the break-even age for winning and losing generations in this policy experiment turned out to be around 30-35 years.

38

percent, without lowering benefits.44 The long-term income gain to future generations

would be in the order of magnitude of 5 percent of GDP.

Recent numerical studies of pension reform with endogenous factor prices are based

mainly on variations of the Auerbach and Kotlikoff (1987) simulation model.45 Kotlikoff

(1996, 1998) carried out a full general equilibrium analysis of a shift to a fully funded

system in the U.S., assuming endogenous capital formation, labor supply and factor

prices. As expected, the gain to future generations from such a shift would be particularly

large when the linkage between contributions and benefits in the old system is weak

(hence starting close to position I in our Figure 1), when other taxes are high and the

transition is financed by taxes on consumption rather than income or labor earnings.46 For

most simulations, Kotlikoff reports long-term increases in GDP of about 10 percent.

Typically, the contribution rate would have to be raised initially, but will eventually end

up a few percentage points lower than the initial level. Depending on the method of

financing old claims, on the initial degree of linkage, and on whether the transition

generations are compensated or not, he reports increases in steady-state lifetime utility of

between 1 and 10 percent. However, if taxes are raised abruptly for early generations

(that is, if there is extreme front-loading), labor supply is distorted to such an extent that

all subsequent generations may lose from the pension reform. This result illustrates the

trade-off between forced saving and distorted work incentives.

The earlier mentioned general equilibrium study by the European Commission (2001)

analyzes a shift to a fully funded system in the European Union. The study is based on a

model by Kieran McMorrow and Werner Roeger (2002) and differs from the Auerbach-

44 In similar calculations for the EU, Feldstein (2001, p. 5) reports that the future payroll tax could be cut from 30 to 9.45 percent in the long run by shifting to a fully funded system. 45 See Laurence J. Kotlikoff, Kent A. Smetters and Jan Walliser (2001) for a comprehensive list of references to the simulation literature. 46 In economies with high taxes on income, one reason why consumption taxes are more favorable than other taxes is that it may be advantageous to smooth taxes over many tax bases. Another argument may be that consumption taxes do not distort saving decisions. A third reason is that a consumption tax functions as a capital levy, which is non-distortive – provided that it is not expected to be repeated. The case for a consumption tax is further strengthened if there is no constraint to keep the living standard of the old pay-as-you-go pensioners unchanged. The capital-levy property of such a tax then hits the pensioners as well.

39

Kotlikoff framework in assuming a non-competitive (unionized) labor market. If a

transition to a fully funded system were financed by a “double contribution”, the total

contribution rate (in our terminology, τ θ∗ + ) would initially have to be raised to 28

percent, although it would gradually drop to about 20 percent in 2050 and to 17 percent in

2100 (European Commission, 2001, p. 208). This experiment would lead to a long-run

increase in GDP of 5 percent, i.e., a change of the same order of magnitude as reported by

Feldstein and Samwick (1998) and Kotlikoff (1996, 1998) for the United States. The EU

Commission has pointed out that this GDP increase is significantly smaller than what

would result if the effective retirement age were raised to 65 years while maintaining the

pay-as-you-go system (which gave a GDP increase of 13 percent; p. 199). If a higher

retirement age is combined with funding, a modest additional GDP gain can be achieved.

Is it then possible to compensate the generations working immediately after the reform,

so as to bring about a Pareto improvement by shifting to a fully funded system? Kotlikoff

(1996, 1998) studied this possibility for several different scenarios. In the most favorable

case (modest front-loading, zero linkage in the old pay-as-you-go pension system

combined with old claims financed by a consumption tax), a Pareto-sanctioned shift to a

fully funded system is possible. In this case, steady-state lifetime utility would increase

by 4 percent.

Hirte and Weber (1997) carried out simulations for Germany, also based on the Auerbach

and Kotlikoff (1987) framework. The initial conditions in their study are characterized by

positive but weak linkage between contributions and benefits (with 90 percent as a tax),

reflecting the current German pay-as-you-go system, and a public good financed by taxes

on capital, consumption and income. In contrast to Kotlikoff (1996, 1998), Hirte and

Weber use distortionary (income or consumption) taxes not only to honor the old pay-as-

you-go claims, but also to compensate losers during the transition. When compensating

all losers, they find that an increase in steady-state welfare, expressed in wealth

This helps explain why simulation models arrive at the result that the highest steady-state welfare is obtained when the transition is financed by consumption taxes.

40

equivalents, of 7-8 percent, can be achieved by combining tax smoothing and a shift of

the tax base to income or consumption taxes.47

Raffelhüschen (1993) concludes that Germany could achieve a modest efficiency gain

from shifting to a fully funded system by using a combination of borrowing and taxes to

finance the old pensioners and by compensating losers. D. Peter Broer, Ed W. M. T.

Westerhout and A. Lans Bovenberg (1994) use a variant of the Auerbach-Kotlikoff

model to analyze a reduction in the size of the Dutch pay-as-you-go system. They show

that a Pareto improvement is possible when the pay-as-you-go pensioners are

compensated by some fraction of the returns from the funded system. This gain is

achieved mainly because there is only a weak link between contributions and benefits in

the old pay-as-you-go system.

Note, however, that in the models discussed above, a Pareto improvement is possible

only if the old pay-as-you-go system did not already comprise a tight link between

contributions and benefits. Shifting from the neighborhood of position I to position IV in

figure 1 may well result in a Pareto gain,48 but the same gain can be achieved without

funding, simply by shifting from position I to II.49 Adding a vertical move from position

II to position IV would not yield any further efficiency gains since the claims of the old

pay-as-you-go pensioners still have to be honored.

Finally, there is the dilemma of specifying the individual’s intertemporal preferences in a

realistic manner. It is somewhat paradoxical to analyze pension reform assuming

traditional, exponential discounting when the existence of mandatory pension systems has

47 As shown by Johann K. Brunner (1996), the possibility of a Pareto improvement is smaller if there is intra-generational heterogeneity. 48 Moving from a completely non-actuarial pay-as-you-go system to an actuarially fair, fully funded system, with the old claims financed by the benchmark vector ,θ will reduce the tax wedge on labor by

(1 ) /(1 );G Rτ + + cf. Subsection 4.1. This would not have any direct impact on aggregate saving. Implementing instead a somewhat front-loaded θ vector could result in some reduction in the tax wedge, as well as an increase in aggregate saving. 49 Auerbach and Kotlikoff (1987, p. 158 ) have estimated the efficiency gain for the US economy of moving from I to II. They find that such a shift increases full lifetime resources by between 7.6 and 15.1 percent depending on how other government spending is financed (namely by proportional or progressive income taxes).

41

been motivated by the fact that individuals are myopic, for example expressed in

hyperbolic discounting. This raises potentially important issues for future research.50

5.6 A Question of Framing?

So far, we have identified two types of pension reform that may create welfare gains to

society. First, strengthening the linkage between contributions and benefits may result in

a Pareto improvement due to less distortions in the labor market. Second, a shift to a

funded system may increase aggregate saving, which in turn will increase aggregate

income over generations if the return on real capital happens to be higher than the market

interest rate. Only the first measure, however, is intrinsically related to the design of the

pension system. The second could, in principle, also be achieved by ordinary fiscal policy

measures without changing the pension system. Thus, the second type of pension reform

may be regarded as a way of framing policy measures that would otherwise be politically

infeasible. Another example of framing is when a pension reform is combined with

changes in the tax base or in the time profile of taxes (in the fashion discussed in Section

5.4).

Apart from Pareto welfare improvement (via less labor-market distortion), there is the

issue of intergenerational redistribution. This could also be achieved by general fiscal

policy measures. A shift to a funded pension system as a means to redistribute income

across generations could, therefore, also be regarded as a matter of framing. For instance,

changes in the intergenerational income distribution in favor of future generations may be

achieved by raising taxes today in order to amortize public debt. If such a measure is not

politically feasible, a pension reform is a potential vehicle for de facto achieving the

desired objective.

All this leads us into deep water. For example, who really wants higher national saving

and a redistribution of income in favor of future generations? Obviously not the majority

of the electorate; otherwise, it would not have been necessary to deceive it by disguising

50 For attempts to address these issues in connection with retirement decisions, see Peter A. Diamond and Botond Köszegi (2002) and Ayse Imrohoroglu, Selahattin Imrohoroglu and Douglas H. Joines (2002).

42

the contemplated redistribution. In any event, the scholarly debate on the pros and cons of

a shift to a funded system usually does not invoke a need to frame redistribution in terms

of pension reform.

6. Risk and Risk Sharing

Up to this point, we have neglected risk and risk sharing. A primitive way of introducing

risk would be to interpret the interest rate, R, and the growth rate in the tax base, G, as

certainty equivalents. Indeed, this is what we have implicitly done so far. A more explicit

treatment of risk is called for, however, by including variances and covariances of the

rates of return. This implies that we regard pension claims as part of an individual’s total

asset portfolio (subsection 6.1). The next step is to examine how risk is shared within and

among generations (subsection 6.2). This brings up the third dimension in our

classification of pension systems, namely the distinction between defined contribution

and defined benefit systems.

6.1 A Portfolio Approach

Since a pay-as-you-go system provides a new “asset” (pension claims with an uncertain

yield tied to the growth rate of the tax base), the government solves a missing market

problem. Such a system may, therefore, contribute to a welfare improvement, in the form

of a more favorable trade-off in risk/return space – provided R and G are not perfectly

correlated. In figure 2, curve AA shows the available risk/return combinations when there

is no mandatory pension system at all. We now assume that a pay-as-you-go system is

introduced, and that it is characterized by a risk/return combination corresponding to

point P. If the “pay-as-you-go asset” (the “paygo asset” for short) had been fully divisible

and marketable, like a so-called “Shiller bond”,51 the new frontier available to the

51 Shiller (1993) has advocated the introduction of a bond whose yield is tied to the growth rate of GDP. Although this does not exactly correspond to a paygo asset, it is fairly close. To the best of our knowledge, this proposal has not yet been implemented in any country. Bohn (2002) has advocated government bonds

43

investor would be located above the AA frontier. This is a direct consequence of adding a

new “asset” that is not redundant or dominated by a combination of existing assets. We

call this hypothetical frontier (not depicted in figure 2) the “Shiller frontier”.

[Figure 2 here]

In reality, however, a pension asset in a mandatory pay-as-you-go system is indivisible

and non-marketable. For some individuals, the pay-as-you-go system will be too large,

for others too small, as compared to the amount of Shiller bonds he would choose

voluntarily. Thus, the efficient frontier associated with a mandatory pay-as-you-go

system is located below the Shiller frontier. Whether it will be above or below the AA

frontier depends on three factors: the size of the pay-as-you-go system, the wealth of the

individual, and the covariance between the paygo asset and other assets. In figure 2, we

have drawn the efficient frontier, depicted by the curve CC, above the AA curve – but it

could just as well be below AA. A non-constrained individual will then choose a

combination of the risk-free asset, traditional risky assets, and the mandatory paygo asset

– a position located somewhere on the capital-market line BB' in the figure.

For a liquidity-constrained individual, on the other hand, the introduction of a pay-as-

you-go system means that he will be confined to point P. According to the government’s

revealed preference, point P is superior to point O, which the liquidity-constrained

individual would choose in the absence of a mandatory system. Indeed, this is one reason

why a pay-as-you-go system is introduced in the first place.

What happens now if the government decides to shift to a fully funded system? If the

shift is total, the paygo asset disappears. A non-constrained individual can then choose a

risk/return combination along the capital market line BB that is tangent to the original

efficiency frontier AA – just as if there were no mandatory system whatsoever; see

footnote 12. Theoretically, this conclusion holds not only if the individual can choose

indexed to wages and demographic variables; such bonds would constitute a marketable and divisible paygo asset.

44

among many competing pension funds, but also if there is a single government-operated

fund – provided that well-functioning derivatives markets exist, and that the individual is

able and willing to transact in these markets. This is probably not a very realistic

assumption, however.

It is even more difficult for a liquidity-constrained individual to pursue fully offsetting

transactions when there is a central pension fund. For instance, he may be unable to put

up the margin required to make the necessary transactions (like selling stocks short); he is

also likely to be quite unfamiliar with the functioning of derivatives markets. Therefore,

the portfolio choice of a central fund will probably affect liquidity-constrained

individuals more than those who are non-constrained.

At this point, it is important to recognize that the rate of return should be net of

administrative costs. It is generally agreed that administrative costs tend to be much

higher in funded than in pay-as-you-go systems. The cost differential may well be

between 0.3 and 1.5 percent of pension wealth, with the lower figure referring to index

funds. In fact, the costs have been even higher in Chile and the U.K., which has lead to

severe criticism. However, administrative costs can be cut. One way is to require all

pension funds in a mandatory system to be confined to index portfolios; another is to put

a cap on the administrative costs of individual funds, perhaps thereby forcing them to

choose index portfolios.52

Since R and G are not perfectly correlated in the real world, portfolio diversification is an

argument for a partial rather than a total shift to a funded system. Indeed, this is the

solution recently chosen by a number of countries (see section 7). But even such a mixed

system restricts an individual’s choice since he faces a government-imposed restriction

on the amount of paygo asset to be held. Whatever composition of the mixed system the

government chooses, the amount of the paygo asset may be too large for some individuals

52 For information about administrative costs, see Olivia S. Mitchell (1998), Mamta Murthi, J. Michael Orszag and Peter R. Orszag (1999) and Diamond (1999).

45

(in particular, some low-income earners) and too small for others (in particular, some

high-income earners) – as in the case of public goods.

Rate-of-return risk in pension systems is associated not only with fluctuations in the

growth rate of the tax base and the rate of return in financial markets, but also with

political risk. When discussing the latter, it is important to realize that new political

interventions in the pension system do not always increase the risk for the individual. If

the economy is unexpectedly hit by a shock that was not contemplated when the system

was designed, early intervention may reduce the likelihood of more far-reaching

interventions in the future. Thus, it is useful to distinguish between policy measures that

counteract the consequences of exogenous macroeconomic shocks (“market risk”) and

policy measures undertaken to placate various interest groups or political parties.

We argued in Section 4.3 that political interventions are less likely in pension systems

with strong property rights. Hence, political interventions would be less likely in quasi-

actuarial than in non-actuarial pay-as-you-go systems, and even less likely in actuarially

fair, fully funded systems. But political risk is not absent in the latter type of system. It

takes two forms. One concerns the allocation of the pension fund assets to different

sectors, regions and firms. The problem here is that politicians may intervene in this

allocation, motivated by party politics. In some countries, such interventions have, in fact,

resulted in very low (and in some cases negative) return on government-controlled

pension funds; see World Bank (1994, p. 95). Political risk is likely to be lower in the

case of decentralized, privately run funds with individual accounts than in a single,

central fund operated by the government; the property rights are likely to be stronger,

thereby limiting the risk for political intervention in the management of the funds.53 In

principle, the political risk of fund management may, however, be diversified by having

several government-operated funds, rather than one fund, with different politicians in

different funds.

53 But not even privately managed funds with individual accounts are wholly immune to political intervention. Historically, some governments have imposed restrictions on the portfolios of such funds, mostly in order to favor government “pet” projects, or have unexpectedly introduced extra taxes on the

46

A related issue is who should exercise ownership in companies where pension funds own

shares, for instance, by making political appointments to the boards of these firms. If

government-initiated pension funds are very large as compared to a country’s economy,

there is a risk of vast nationalization and politization of the national economy. Here, too,

the risk of political abuse is probably smaller in a system with competing, decentralized

private funds. Higher administrative costs associated with decentralized fund

management then may be regarded as the price to be paid for minimizing the risk of

misuse of political power. The importance of these considerations is illustrated by the

sheer size of the funds involved. If all government-operated pension systems were fully

funded, the funds would correspond to 200-300 percent of GDP. This would basically

correspond to the size of the total stock of real capital.

Regardless of whether the political risks are higher or lower in a funded system than in a

pay-as-you-go system, it is reasonable to assume that they are different and therefore not

completely correlated. Differences in political risk provides an additional argument for

diversification of pension claims, i.e., for a mixed system, combining pay-as-you-go and

funded systems, as argued above.

6.2 Risk Sharing

Pension systems distribute risk differently along three dimensions: among generations,

within generations, and over an individual’s life cycle. A comprehensive analysis of risk

and risk sharing in all these dimensions would require a quantitative general equilibrium

analysis. Still, some insight can be gained from theoretical considerations, which we

pursue here; this issue is discussed in some detail in Lindbeck (2000). Let us begin with

the distribution of risk among generations.

Intergenerational risk. Issues of intergenerational risk sharing are particularly apparent in

the context of pay-as-you-go systems. In such a system of the defined-contribution type,

returns of pension funds when these returns have been regarded as particularly conspicuous (Denmark and Sweden in the 1980s and 1990s are examples).

47

hence with a fixed contribution rate, fluctuations in the real wage rate w influence the

disposable income of both workers and contemporary retirees in the same direction. This

means that risk in w is shared between workers of generation t and individuals of

generation t-1 when retired. Abstracting from general equilibrium effects, we call this

direct risk sharing. It does not take place in either fully funded systems or pay-as-you-go

systems of the defined-benefit type (since pensions in the latter case are either exogenous

or predetermined as a fraction of the pensioner’s earlier income).54 Direct sharing of risk

is also straightforward in the case of fluctuations in the number of workers, n. In a pay-

as-you-go system of the defined contribution type, such fluctuations only affect the

pensions of the preceding generation. Thus, this specific demographic risk is borne by the

retirees. By contrast, in a pay-as-you-go system of the defined-benefit type, workers bear

the entire burden of shocks in both w and n. In fact, in the case of changes in w, they have

to bear a double burden: if w falls, not only will they earn a lower wage, they are also

forced to pay a higher contribution rate in order to balance the pension budget.

We may note that not only the distributional, but also the efficiency effects of shocks

differ between defined-contribution and defined-benefit systems. If the latter type of

system is hit by a negative shock in G (regardless of whether it is induced by a change in

w or n), the tax wedge necessarily increases since the contribution rate has to be raised.

By contrast, the effects on the tax wedge in a defined-contribution system are more

intricate. In the case of a quasi-actuarial system, where the tax wedge is ( ) /(1 )R G Rτ − + ,

the wedge will certainly increase if G falls. It is, however, important to distinguish

between the current G (which affects the distribution between contemporary workers and

retirees) and the G expected to prevail during the next generation’s working life (which is

relevant for the tax wedge formula). This means that a fall in G that is expected to be

temporary will not affect the tax wedge faced by contemporary workers, even though it

has distributional consequences. Only if the change in G is expected to persist during the

working life of the next generation will it affect the tax wedge of today’s working

generation. Thus, in non-actuarial defined-benefit systems, both temporary and persistent

54 For a discussion of different aspects of risk-sharing, see Shiller (1999), Øystein Thøgersen (1998) and Andreas Wagener (2001).

48

changes in G will influence the tax wedge, via changes in τ . By contrast, in quasi-

actuarial defined-contribution systems, only persistent changes in G will affect the tax

wedge, via changes in the expected value of G.

There are also indirect risk-sharing mechanisms associated with general equilibrium

effects. For example, in a funded system, a fall in w, n or the number of hours of work, ,

will reduce the resources available to the young to buy the unloaded assets of the elderly.

This lowers asset values and the return on previous pension savings. Reasoning along

these line has led some authors (Barr 2000, and EU Commission 2001, p. 184) to argue

that the risks are, at least in principle, rather similar in pay-as-you-go and funded systems.

But this holds only for a closed economy. In an open economy, domestic financial

instruments are much less affected by shocks to the income of the active population.

Moreover, since domestic pension funds can diversify by investing in foreign assets, a

funded system in a small open economy can be virtually immune to domestic shocks to

demography and productivity. By contrast, a pay-as-you-go system is, by definition,

entirely dependent on the domestic economy.

If high priority were given to avoiding large changes in the relation between incomes of

workers and contemporary pensioners due to various shocks, a convenient solution would

be a system with a fixed ratio between the incomes of these groups, b w . Such a

system, proposed a long time ago by Richard A. Musgrave (1981), requires that τ be

continuously adjusted to guarantee financial balance. The individual may still receive

pension benefits in proportion to previous contributions, and thus the system could be

said to have actuarial elements.

/

A special type of intergenerational, or rather inter-cohort, risk is related with

annuitization. This risk arises when a stock of pension wealth is transformed into an

annuity, i.e., a flow of pension benefits after retirement. Even individuals of

approximately (although not exactly) the same age could face very different capital-

market situations at the time of retirement, and hence receive quite different pension

annuities.

49

The annuitization risk could be quite substantial. For instance, Gary Burtless (2000) has

shown that with fixed annuities, U.S. workers retiring in 1974 would have received only

half the replacement rates as workers retiring in 1968.55 This risk may be reduced by

providing a flexible annuity instead, so that pension wealth remains invested in the

individual’s account throughout the retirement period (although it will gradually be

reduced as time goes by). This means that the annuitization risk would be replaced by an

ordinary rate-of-return risk.56 Indeed, this is often the way annuitization risk is dealt with

in private pension schemes, as well as in some funded government-run schemes.57

Uncertainty about remaining life expectancy, i.e., longevity risk for an individual’s

cohort, is another element of the annuitization risk. The annuity could either be kept

constant after retirement, or be gradually adjusted to changes in the cohort’s life

expectancy during the retirement period. In the former case, the cohort longevity risk is

borne by the insurance provider after retirement. In the latter case, when the annuity is

gradually adjusted to changes in life expectancy, the individual bears cohort longevity

risk during his entire lifetime.

Intragenerational risk. While defined benefit systems (regardless of whether they are

pay-as-you-go or fully funded) do not contribute directly to risk sharing among

generations, they can certainly function as a risk-sharing device within generations. For

instance, in the case of a basic pension, fluctuations in earnings do not result in

corresponding fluctuations in pensions. The risk-sharing properties of the pension system

55 A similar problem emerges if the pension portfolio is shifted once-and-for-all from equities to bonds. Thomas E. MaCurdy and John B. Shoven (1999) study an asset swap by a trust fund from bonds to stocks in a given year. The probability that such a swap will be a failure is found to be 25-30 percent (p. 20-21). 56 Martin S. Feldstein and Elena Ranguelova (2001) report that with variable annuities, this risk could be rather modest. For instance, a 67 year old has a 15 percent chance of receiving less in a fully funded scheme (60 percent stocks and 40 percent bonds) than under present US pay-as-you-go rules. The probability of receiving 50 percent less is roughly 2 percent (table 1 and p. 15). 57 A more radical solution would be to hand over the entire pension wealth to the individual at the time of retirement. He could then choose his own investment strategy and the consumption profile during retirement. Such a solution, however, would fail to fulfill some of the objectives of a mandatory system, such as dealing with free-riding and myopia.

50

are then similar to those of a progressive income tax.58 Due to specific institutional

arrangements, however, certain elements in defined benefit systems in the real world

accentuate rather than mitigate intragenerational income risk. One example is when the

pension is tied to earnings during the x last years of work, rather than to lifetime earnings.

Individuals who turn out to have low incomes late in life will then suffer a low income

when retired.

Another type of intragenerational income risk is associated with family dissolution.

Historically, non-actuarial pension systems have included simple rules for allotting

incomes among family members after the breakup of a family, basically in the form of

pensions to widows and their children. By contrast, in a (quasi-) actuarial system with

individual accounts, the pension is closely tied to the individual income earner. Without

special arrangements, income risk due to the dissolution of a family is therefore larger in

systems with individual accounts than in many existing pension systems. The family

member with the lower market income, usually the woman, would therefore be exposed

to a higher risk in a pension system with individual accounts. One remedy might be to

give each spouse a property right to the other’s pension wealth. This is straightforward in

the case of formal marriages, where similar arrangements are already in place for other

types of property, but is more difficult to implement in the case of cohabitation.

An additional aspect of the distribution of intragenerational risk in the case of funded

defined contribution systems is that the return risk will vary among individuals if there

are many funds to choose among, rather than one central fund. Depending on differences

in skill and luck, otherwise similar individuals may end up with widely different

pensions. This illustrates the trade-off between freedom of choice and ambitions of the

authorities to achieve an even distribution of income among pensioners.

Risk distribution over the life cycle. Pension systems may redistribute not only income

but also income risk over the life cycle. It is useful to discuss this issue in terms of the

58 Kjetil Storesletten, Chris I. Telmer and Amir Yaron (1999) have computed the insurance value of this type of risk sharing. For parameters assumed to be realistic, the welfare gain from reduced income risk in

51

renowned “veil of ignorance”, i.e., the notion that an individual does not yet know his

type, as reflected in future earnings, when he takes important decisions. In a defined

contribution system, there is uncertainty concerning w, while the fixed contribution rate

τ may be known. There is also uncertainty about the return on contributions, since R and

G are not guaranteed in advance. By contrast, in a defined benefit system, there is

uncertainty not only about w but also about τ , since the latter has to be adjusted to

achieve budget balance. On the other hand, the pension benefit may be known in

advance. Indeed, with a fixed benefit b , there is no uncertainty at all concerning the

pension, while in a defined benefit system with a fixed replacement rate (such that

b wγ= ) there is uncertainty about the pension behind the veil of ignorance solely as a

result of uncertainty about w. All this means that a pension reform represented by a shift

from a defined benefit system to a defined contribution system will remove one source of

uncertainty from the first period of an individual’s life (uncertainty about τ ), but

introduce a new source of uncertainty in the second period of life (uncertainty about R or

G). It is difficult to judge a priori whether such a shift in the distribution of risk elements

over the life cycle is favorable or not. Presumably, this depends not only on the assumed

utility function, but also on the properties of the stochastic processes underlying the

shocks.

Modigliani and Ceprini (2000) have suggested a solution to some of these risk problems.

They envisage partly funded, actuarially fair system with a single fund investing in

marketable securities and with equities allocated to a broad stock-market index. Since

there is only one fund, intragenerational risk associated with many different funds, with

different returns, is avoided – at the cost of abolishing portfolio choice according to

individual preferences. Intergenerational risk is removed by a guaranteed real rate of

return of five percent per annum. The annuitization risk of retirees (indeed, inter-cohort

risk) is thereby also removed. The five-percent return is achieved through a swap

between the fund and the Treasury; in exchange for the return derived from the fund’s

portfolio, the Treasury pays a fixed real return of five percent.

the current U.S. social security system corresponds to between one and two percent of lifetime income.

52

The proposal combines features from defined benefit and defined contribution systems. It

is defined contribution, and actuarial, in the sense that pensions are based on the

individual’s paid contributions, that the rate of return is R, and that the contribution rate is

fixed. But it has elements of a defined-benefit system in that throughout the individual’s

lifetime, he has reason to be confident about the pension benefits he has earned so far.

This certainty, however, is acquired at the cost of greater uncertainty for taxpayers, who

have ultimately issued the five percent return guarantee. A remaining problem with a

central fund, of course, is that it is vulnerable to political risk – in particular, the risk

associated with the exercise of ownership and control of firms.

In highlighting the possibilities of diversifying risk in pension systems, we have pointed

out that such diversification can be accomplished in several dimensions. It is, in general,

advantageous to combine funded and pay-as-you-go systems, since they have different

risk characteristics, with respect to both market risk and political risk. It is probably also a

good idea to combine a defined contribution system with some elements of a defined

benefit system. Defined contribution systems provide (direct) risk sharing among

generations, while defined benefit systems may provide risk sharing within generations.

Indeed, most countries offer a basic pension (at a rather low level) as an important

element of the entire mandatory pension program.

7. Concluding Remarks

In this paper, we have tried to systematize and clarify various issues that have been

prominent in recent discussions of pension reform. To this end, we have applied a three-

dimensional classification of pension systems: actuarial versus non-actuarial, funded

versus pay-as-you-go, and defined contribution versus defined benefit systems. Each of

these dimensions is associated with a special aspect of pension reform: labor-market

distortions, aggregate saving, and considerations of risk, respectively.

53

We have emphasized that efficiency gains in the labor market can be achieved by

strengthening the link between contributions and benefits in a pay-as-you-go system.

Indeed, in a quasi-actuarial system, where the individual’s marginal return on mandatory

pension saving is equal to the growth rate in the tax base, the labor-market distortion is

minimized. We have shown that this opens up a possibility of a Pareto improvement.

Moreover, it is commonly held that a shift to a quasi-actuarial system with an exogenous

contribution rate (i.e., a contribution-based system) will increase the financial stability of

the pension system, in the sense that politicians then have not made any promises

concerning future pension benefits.

What, then, are the gains from shifting from a quasi-actuarial to an actuarially fair, fully

funded system? No further efficiency gains are possible in the labor market if the claims

of the old pay-as-you-go pensioners are granted. This explains why, under certain

circumstances, a shift to a fully funded system would be a “wash” in terms of aggregate

income across generations. We discuss three cases where this conclusion does not hold.

The first case is when the return on real capital is higher than the market interest rate,

which means that an aggregate income gain across generations could be achieved by

higher capital formation. There are two ways to bring about such increased capital

formation in connection with a shift to a funded system. One is to squeeze both liquidity-

constrained and non-constrained individuals, by making the extra tax, necessary to grant

the old pay-as-you-go claims, front-loaded. This means that the tax weighs more heavily

on earlier than on later generations after the reform. The other method to increase

aggregate capital formation is to squeeze only liquidity-constrained individuals, which

can be achieved even without front-loading. We show, however, that increased capital

formation by mandatory saving, regardless of who is squeezed, does not result in a Pareto

improvement.

The second case where a shift to a funded system is not only a “wash” occurs when we

use an intergenerational discount rate that is lower than the market rate. We show,

however, that such an aggregate income gain can be brought about only if the new tax,

54

used to finance the old pay-as-you-go claims, is front-loaded. Such a reform certainly

does not imply a Pareto improvement, since early generations have to be squeezed also in

this case.

A third case concerns issues of risk. Although the introduction of a pay-as-you-go system

creates a new type of asset, the compulsory nature of the system will force some

individuals to hold unbalanced portfolios, with the “paygo asset” constituting too large a

part of their entire portfolios. Replacing part of that asset with funded pension claims will

then lead to better portfolio diversification for those individuals. This is the case, in

particular, if the pension funds are allowed to invest in foreign assets, because pensions

would then be less exposed to what happens in the domestic economy. Since the political

risk is also likely to differ between pay-as-you-go and funded systems, this further

strengthens the portfolio diversification argument for a mixed system.

We also discuss how different pension systems distribute risk among generations, within

generations, and over an individual’s life cycle. It turns out that the distinction between

defined-contribution and defined-benefit systems is crucial for such an analysis. For

instance, as may be expected, a defined-contribution system tends to shift relatively more

risk to the retired population, while a defined-benefit system shifts relatively more risk to

the workers. Risk sharing among generations is less obvious in funded than in pay-as-

you-go systems, though it may occur via general equilibrium effects in countries where

the domestic capital market is not fully integrated internationally.

Several quantitative simulations suggest that a shift from a pay-as-you-go to a fully

funded system can be designed in such a way that rather modest sacrifices of early

generations will result in large gains for future generations. Whether such a reform is

worth undertaking then depends on preferences concerning the intergenerational

distribution of income. Regardless of the reasons for redistribution in favor of future

generations, this can, however, be accomplished by ordinary fiscal policy measures, quite

outside the realm of pension reform. Why, then, is pension reform often suggested as a

means of increasing domestic capital formation and redistributing income in favor of

55

future generations? The answer is presumably that pension reform is a way of framing

policies that may otherwise be politically difficult to achieve, such as by general fiscal

policy. Indeed, empirical research in economic psychology has shown that framing

influences individuals’ perception of policies with identical content.

How, then, should we characterize recent changes in the mandatory pension systems of

various countries? There is a strong tendency today to reform existing pension systems in

the direction of increased actuarial fairness, and to combine pay-as-you-go and funded

elements. The reforms also reflect a trend towards individualization. Since pension

systems with strong linkage require individual accounts with continuous reporting of the

individual’s pension wealth, whether notional or actual, the pension wealth becomes

more transparent, equipped with stronger property rights, and portable across national

borders. Greater individualization probably reflects three contemporary changes in

society: more individualistic preferences (as empirically studied by Ronald Inglehart),

increased globalization, and the new information technology that facilitates handling of

individual accounts. It is interesting to note that the trend towards individualization is not

limited to government-operated pension systems. Occupational pensions have also

undergone a transition from employer-provided defined benefit systems to funded

systems with personal retirement accounts.

In order to accommodate the demand for more individualized social security, the

individual could be given greater freedom in deciding when to use the mandatory pension

savings during the life cycle. This does not only imply a flexible retirement date, but also

arrangements for utilizing part of the savings for specific purposes during working life,

such as paying for an adult education, buying a home, or starting a firm.59 Such

arrangements can be made in funded as well as unfunded systems; the two most well-

known systems, namely those in Singapore and Malaysia, are funded, however.

59 An early proposal along these lines is that of Gösta Rehn (1961). More elaborate plans have been developed by Stefan Fölster (1999) and J. Michael Orszag and Dennis S. Snower (1999).

56

Against the backdrop of our analysis above, let us take a look at actual reforms in various

countries. 60 We start with parametric reforms, which are often pursued in order to

restore financial stability. Next, we move on to systemic reforms.

Most parametric pension reforms during the last decades have been designed to

guarantee better long-term financial stability of the pension systems. A common measure

has been to gradually increase the contribution rate τ . Indeed, in many countries it has

been raised from a few percentage points, when the systems were launched, to 15 or 20

percent today.61

In the light of political difficulties and concern over economic distortions connected with

increases in the contribution rate, we have, however, recently seen a trend towards

financial consolidation via cuts in benefits – often using rather innovative methods. The

purpose has then been to reduce the capital value of benefits in order to respect the

system’s intertemporal budget restriction. In some cases, this has been achieved by

reducing the nominal value of yearly pension benefits (either by cutting a flat benefit or,

in the case of earnings-based pensions, reducing the replacement rate). This has recently

been done in, for instance, Greece, Hungary, Italy, Korea, Portugal and Switzerland. New

Zealand has used a more indirect method to reduce the replacement rate, namely to cut

the ratio of pensions to the average wage of contemporary active workers.

There are also examples of selective benefit cuts, hitting only part of the population.

Some countries have imposed stricter eligibility rules for receiving any pension at all.

Belgium, Germany and the U.S. have increased the number of years necessary to qualify

for a pension, and Iceland and Italy have done the same for public-sector employees.

But it has probably been more common to reduce the real value of pension benefits by

shifting from wage indexation to price indexation of pension benefits. Basically, this has

60 Our examples of changes in pension systems are mainly based on from OECD (2000) and the papers in Martin S. Feldstein and Horst Siebert (2002).

57

been done connection with recent pension reforms in Sweden and Japan. The pension

reform in Germany in 2000 combines changes in wage and price indexation. A shift from

gross to net wage indexation was followed by a shift to price indexation, both with the

explicit purpose of limiting future increases in contribution rates (Bonin 2002). Another

way is to manipulate the price index, for instance, by excluding components that have

shown a tendency to rise particularly fast (like oil, in the 1980s).

Without touching yearly benefits, their capital value has instead been reduced in some

countries by raising the retirement age. Examples are Germany, Italy, Japan, New

Zealand and the U.S. In some cases, higher retirement age has been limited to particular

groups, such as women (in the U.K. and Belgium) or public-sector employees (in Italy).

In fact, raising the effective retirement age is a powerful way to restore financial stability.

A double effect is then achieved: a simultaneous increase in the number of workers, and a

decrease in the number of eligible pensioners. In the previously mentioned study by the

European Commission (2001) on the consequences of raising the effective retirement age

to 65 years, it is concluded that an otherwise necessary increase in the social security

contribution from 16 percent in 2000 to 27 percent in 2050 could thereby be limited to

20.5 percent (pp. 191-199). This result should be compared to an outright reduction in

benefits. For instance, according to the EC study, a drastic reduction in the replacement

rate from 74 to 58 percent would still require an increase in social security contributions

to 22.7 percent by 2050 (p. 198).62

In response to the dramatic fall in labor-force participation among elderly workers

(Gruber and Wise, 1999a, 2002), many developed countries have stiffened the rules for

61 In some countries, the contribution rate has been kept down by channeling general tax revenues to the mandatory pension system. Germany is one example, where in the late 1990s around 27 percent of pension benefits were financed in this way (Holger Bonin, 2002, p. 1). 62 The intergenerational distribution effects would be drastically different in these two experiments. According to the study, the consumption of the working-age population would increase by 6.4 percent while that of pensioners would fall by 7.6 percent by 2050 in the case of a reduced replacement rate. By contrast, in the case of a higher effective retirement age, the consumption of working-age population and pensioners would increase by 10.8. and 16.3 percent, respectively. The favorable effects on the consumption of pensioners are, of course, the result of a longer working career (European Commission 2001, pp 198-199).

58

early retirement, by either raising the minimum age for, or reducing the subsidies to, early

retirement. Germany and Italy have implemented both types of changes. Of course,

countries whose systems have recently been rendered more actuarially fair have

automatically reduced existing subsidies to early retirement. Some countries have also

limited the access to various “pathways” to early retirement, including disability pensions

and the transformation of long-term unemployment among older workers into early

retirement. For instance, the Netherlands has considerably stiffened the rules for

disability pensions, while the pathways via long-term unemployment have been partly

closed in Austria, Denmark and Germany. Another way of limiting early retirement has

been to facilitate part-time rather than full retirement.63

Whatever methods are used to make pension benefits less generous, politicians have often

chosen either to postpone the implementation of cuts, or to phase in the cuts slowly over a

long period of time; these empirical regularities have been emphasized by John McHale

(1999). The latter option seems quite reasonable in order to give people time to adjust to

new rules. But postponing implementation raises the risk of time inconsistency; future

governments might continue to postpone the cuts.

So much for parametric changes. Turning now to systemic pension reforms, we illustrate

a few such reforms in figure 3.64 For instance, pre-funding (i.e., raising the contribution

rate in anticipation of future demographic changes) in the U.S. and Canada social security

systems may be regarded as a (modest) systemic change in the sense of a move in the

direction of a funded system, though still with very weak actuarial elements. 65 This is

illustrated as an upward movement of the U.S. and Canadian systems in the figure.

Similar moves has been undertaken in France, Ireland and the Netherlands. Moreover, in

the late 1990s, various proposals to add an actuarially fair, fully funded element to the

63 This works both ways, stimulating workers to choose not only part-time retirement instead of full retirement, but also part-time retirement instead of full-time work. 64 The illustrations are only schematic; an interesting research project would be to pinpoint the countries with more empirical precision. 65 One reason for regarding this as a systemic change is that there would be a large increase in the trust fund relative to the annual expenditures of the system. In an “intermediate cost” projection, this relation will have increased from about 25 percent in 1985 to about 250 percent in 2015 (Edward M. Gramlich, 1998, p. 32).

59

U.S. system were vividly discussed – with considerable controversy as to whether the

fund(s) should be centralized or decentralized (see the Advisory Council on Social

Security, 1997).

[Figure 3 here]

Several countries (e.g., Italy, Latvia, Poland and Sweden) have recently moved from

quite non-actuarial pay-as-you-go to quasi-actuarial systems with notional accounts. Such

schemes are often combined with partial funding with individual accounts (see Mats

Persson 1999, and Louise Fox and Edward Palmer 2001). Russia is planning a similar

reform. Chile, Argentina and Mexico have made a full shift from non-actuarial pay-as-

you-go to actuarially fair, fully funded systems (Diamond and Valdés-Prieto 1994). These

countries have simultaneously equipped their funded systems with government

guarantees that individual retirees will receive no less than in the previous pay-as-you-go

system.

Instead of shifting to more funding in their mandatory systems, some countries (mainly

the United Kingdom and Germany) have recently encouraged private pension solutions.

In the U.K., the supplementary earnings-related pension system (SERPS) from the 1970s

was reformed in the 1980s by allowing individuals to “contract out”. In the 1990s, this

contracting-out alternative has been made more favorable for low-income groups (Phil

Agulnik 1999). In Germany, downsizing of the original, rather non-actuarial pay-as-you-

go system has been combined with strong subsidization of private, fully funded pensions

(Hirte and Weber 1997). As in the U.K., the actuarial elements of the new system have

been reduced somewhat by special provisions for low-income groups. Since the reforms

in these two countries rely to a large extent on voluntary, rather than mandatory, pension

saving, they are not depicted in figure 3. In the context of the figure, however, arrows

somewhat similar to those of Poland and Latvia could represent these reforms.

Most of these reforms also have implications for the way different types of risk are shared

in connection with disturbances, since they usually imply a change from defined benefit

60

to defined contribution systems. In our terminology, this means that future shocks would

be dealt with by changes in benefits rather than contribution rates. Thus, risk is shifted

from workers to pensioners. Some of these reforms, however, affect the distribution of

risk not only between workers and retirees, but also within these groups. In quasi-

actuarial systems, or in fully actuarial systems with a centralized fund, shocks to the rate

of return (G and R, respectively) affect everyone in the same proportion. By contrast, in a

system with decentralized fund management, shocks affect each individual differently

depending on his choice of fund. Thus we would in this case expect a larger intra-

generational dispersion in realized pensions.

In summary, any pension system has its advantages and disadvantages. It therefore seems

useful to combine different systems, along our three dimensions: actuarial fairness,

funding, and risk sharing. In fact, real-world pension systems, do just that – often by

incorporating four levels of pensions: (i) a basic pension, equal for everyone, or a

guaranteed pension, below which no no-one’s benefits will fall; (ii) a supplementary,

mandatory pension, related to previous earnings or contributions; (iii) occupational

pensions, often the result of collective bargaining; and (iv) voluntary, private pensions.

Recent pension reforms have mainly affected the second of these levels, in some

countries by shifts to quasi-actuarial (sometimes denoted “notional defined-contribution”)

and/or actuarially fair, fully funded systems. The trend towards individualization is

clearly reflected in levels (ii) and (iii) by a shift to individual accounts (notional or real).

Strong expansion of level (iv) is also underway in several countries. This expansion is

mainly spontaneous, but in some countries (e.g., Germany and England) it has been

encouraged by government policies. These reforms do not diminish the need for basic, or

guaranteed, pensions. Quite the contrary; growing reliance on quasi-actuarial and

actuarially fair systems, which in themselves do not encompass any systematic intra-

generational redistributive elements, makes it even more imperative to maintain a safety

net to prevent poverty in old age.

61

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